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  1. pruse

    COMPARE Boston U MSMF vs Rutgers MQF

    Bathrooms at the BBs are about as bad, actually worse in many cases. I work at one so I can vouch for this. If they're like this at respectable banks, can't expect much from a CUNY.
  2. pruse

    COMPARE UCLA MFE vs Columbia MSOR

    There are arguments on both sides. If you don't publish any stats, some will call you opaque, others will just be intrigued and seek out reviews from alumni. And if there's a forum like this where there are enough people willing to give accurate reviews, then there really is no need for stats...
  3. pruse

    Columbia MAFN Columbia MAFN Placement Data for 2010 via Linkedin

    But keep in mind that placement stats can, and often are, doctored. Either they are incorrect or they leave out a part of the story. You must always condition the stats on whatever information you can gather. In fact, placement stats are usually already conditional on some -- often favorable --...
  4. pruse

    COMPARE CMU MSCF (Pittsburgh) vs Columbia MSFE vs Berkeley MFE

    I think he means Joy was going out and interviewing...?
  5. pruse

    COMPARE Columbia OR vs Baruch MFE

    Cool story bro!
  6. pruse

    COMPARE Columbia OR vs Baruch MFE

    Well then I guess they should also know how upset Joy was when Baruch coursework cut into his blogging time. I can't remember if I cried//When they forced him to decide//But something touched me deep inside//The day the blogging died.
  7. pruse

    COMPARE Columbia OR vs Baruch MFE

    It's tough, I know. But when one puts himself on a pedestal, one makes himself a target for inquisition, no? I didn't realize you were a public relations officer for Baruch. If I'd known there were openings I would have submitted an application.
  8. pruse

    COMPARE Columbia OR vs Baruch MFE

    There's a difference between advertising and crushing all dissenting opinions.
  9. pruse

    COMPARE Columbia OR vs Baruch MFE

    What saddens me most about Baruch (especially because I went there and the behavior gives me and others a bad name) is how everyone needs to constantly reiterate how great it is and/or put other programs down in order to lift Baruch. This also happened right after Baruch won RITC. This is not...
  10. pruse

    Baruch MFE My experience with Baruch MFE admission process

    Advait, if I were you I'd count myself lucky for having been spared the difficulties inherent in actually attending the program.
  11. pruse

    COMPARE Columbia OR vs Baruch MFE

    A wise person once said, "if you bite off more than you can chew, be prepared to spit it back out." And don't forget - great things are already known, they don't need an introduction.
  12. pruse

    COMPARE Columbia OR vs Baruch MFE

    "We are Baruch MFE! Resistance is futile! All naysayers shall be smoked!"
  13. pruse

    COMPARE Columbia OR vs Baruch MFE

    Hmm, what if they looked at your older QN posts and some negativity shined through, as Lyosha said? Because if you say something they dislike, you'll often get "smoked."
  14. pruse

    COMPARE Columbia OR vs Baruch MFE

    Lyosha is right about the pre-MFE route, and there's a very good reason for this.
  15. pruse

    COMPARE Columbia OR vs Baruch MFE

    Welcome to the real world. Everyone promises transparency, very few people actually deliver it.
  16. pruse

    COMPARE Columbia OR vs Baruch MFE

    I believe it is included in the 35K, yes. But it used to be 20K. It almost doubled simply because of an "excellence fee" that was tacked on. And judging from the way CUNY operates, more fees and tuition hikes may be right around the corner. Promises, for example, of "guaranteed" interviews that...
  17. pruse

    COMPARE Columbia OR vs Baruch MFE

    Exactly, you shouldn't care what he says about your use of the word 'hyperbole'. Stick to getting your questions answered. Baruch recently started charging an "academic excellence fee" of a couple thousand a semester, so the ROI of the program isn't what it used to be. This used to be one of...
  18. pruse

    COMPARE Columbia OR vs Baruch MFE

    He's trying to derail you and unfortunately he's succeeding a bit. He is trying to troll you because he thinks you're trolling. Don't fall into the trap!
  19. pruse

    COMPARE Columbia OR vs Baruch MFE

    IMHO, I do believe there is a bias towards Baruch on QN. Also IMHO, hyperboles or not, when there are skeletons in closets, the doors should be nailed shut. But that's just IMHO.
  20. pruse

    COMPARE Columbia OR vs Baruch MFE

    He's just trying to derail you with a petty (and incorrect) correction.
  21. pruse

    Question on random number generator

    What is your specialty, might I ask?
  22. pruse

    House of Cards

    The Wire, yes!
  23. pruse

    Question on random number generator

    I was referring to this problem, of course, not approximations of distributions in general. Just staying on topic, that's all. I know plenty of pure mathematics, but I consider myself a problem solver rather than a mathematician. And yes, I am also a quant. Anyhow, I found it ignorant of you...
  24. pruse

    Question on random number generator

    It really does not take "mathematical depth" to understand your solution or to recognize why one should expand about 1, so relax, you sound like a narcissist. Speaking of being a poor sport, I believe it was you who came in here treating everyone with an air of superiority right off the bat.
  25. pruse

    House of Cards

    Agreed. Or Breaking Bad...
  26. pruse

    Question on random number generator

    You actually know some non-trivial math; I'm mildly impressed. What I was referring to, though, was not a series of approximations, which isn't hard to come by, but an exact solution. Still, nice job, you've partially redeemed your previous inane comments.
  27. pruse

    House of Cards

    The show is good, but it's sort of one-dimensional. Each character is good or evil, but not much of a mixture of both. And they're all tragically foolish in their one-dimensionality.
  28. pruse

    COMPARE Columbia OR vs Baruch MFE

    Well, I can't speak for Columbia since I didn't go there. But I went to Baruch. Two things should be noted. 1) Most jobs people get from Baruch are in risk management. 2) The employment stats are a bit dressed up. Stats are presented per graduating class, not cohort. What this means is that...
  29. pruse

    7.7 Jane Street Capital Second Round Interview

    I get what you're saying. However, in your outline above you said "You know that to get to the last roll, you needed to have rolled 50 or less (otherwise, why stop?)." Can you explain this? It seems incorrect to me, as it still disregards the cost of playing. Can you demonstrate that the e.v...
  30. pruse

    7.7 Jane Street Capital Second Round Interview

    no. it's the average of the outcomes E-1, ..., 100
  31. pruse

    7.7 Jane Street Capital Second Round Interview

    yes, but it also depends on the cost of playing, not just what you've rolled...
  32. pruse

    7.7 Jane Street Capital Second Round Interview

    I see what you mean. Upon closer inspection of RRodriguez's argument, I think the misstep is where he says "to get to the last roll, you needed to have rolled 50 or less (otherwise why stop?)" This doesn't take into account the cost of all the rolls up to that point.
  33. pruse

    Question on random number generator

    Yes, you've got it right, you're quite the quick study, aren't you... only a poorly endowed individual such as yourself would hide behind an alias to insult other people. The fact that you use an alias shows you're uncomfortable being yourself, and you dream of being someone else, someone...
  34. pruse

    7.7 Jane Street Capital Second Round Interview

    How can I be so sure? Well, what you're describing is equivalent to the recursion equation I posted above, whose solution is 1223/14.
  35. pruse

    7.7 Jane Street Capital Second Round Interview

    ...The exact answer is 1223/14...
  36. pruse

    Question on random number generator

    I'm sensing some envy here. My sense is you're poorly endowed and dream of being bigger and badder. But you can't have everything. Sorry about that.
  37. pruse

    Question on random number generator

    Useless pure mathematicians, eh?
  38. pruse

    Question on random number generator

    Yeah, I don't yet have a solution for \(F(x)^{\frac{1}{2}}\). It may be that a solution doesn't exist.
  39. pruse

    Question on random number generator

    You need to put your exponents between curly braces for them to come out right, if they're more than one character long: F(x)^{0.5}. The only requirements for a CDF are that it be between 0 and 1, and it go to 0 as you go to -infty and go to 1 as you go to +infty. Since powers of F(x) satisfy...
  40. pruse

    Question on random number generator

    Does it have a specific name? No. Is f(X, Y) unique? That's a good question, I'm actually not sure... Here's another question... We can easily also do (F(x)^3, F(x)^4, ...) using the same approach. Can we also do (F(x)^{\frac{1}{2}})?
  41. pruse

    Question on random number generator

    Why do we care about causality?
  42. pruse

    stock price

    Intuitively it would seem to be 1. The title of this thread is really misleading...
  43. pruse

    Question on random number generator

    If someone posts a problem here, it's usually because they've thought about it all they can, haven't been able to figure it out, and want a solution.
  44. pruse

    Question on random number generator

    Why argue instead of just providing a solution? \(X\sim F(x)\) means that \(P(X\leq x) = F(x)\). Squaring both sides, we may write \(P(X\leq x)P(Y\leq x) = F(x)^2\), where \(Y\sim F(x)\). Assuming that \(Y\) is independent of \(X\), this means \(P(X\leq x \cap Y\leq x) = F(x)^2\). So we just...
  45. pruse

    HFT's good or bad?

    That's the trouble with over-thinking -- it renders everything wrong/right, up/down, left/right all at the same time, which then leads to a kind of madness and/or paralysis. Sometimes you just have to dive right in and go with the flow.
  46. pruse

    Fabricating experience

    fabricate away!
  47. pruse

    2013 Rotman International Trading Competition Result

    Truly! Dan's hard work and determination are quite commendable. The students' too. Congrats all!
  48. pruse

    2013 Rotman International Trading Competition Result

    A bunch of genii, indeed.
  49. pruse

    7.7 Jane Street Capital Second Round Interview

    You can't just discard these, as they are plausible outcomes that need to factor into the e.v.
  50. pruse

    7.7 Jane Street Capital Second Round Interview

    It's the correct strategy, but you must be implementing it wrong. I wrote a quick Matlab script with 1e6 MC simulations and got an e.v. of 87.352, confirming my result above.
  51. pruse

    7.7 Jane Street Capital Second Round Interview

    I don't think anyone is saying it's 87.5. What I was saying above is that it's (\frac{1223}{14} \approx 87.36). What did you get using MC? Note that the recursion we've been discussing assumes that an e.v. optimizing strategy is followed, but it does not tell us what strategy (or...
  52. pruse

    7.7 Jane Street Capital Second Round Interview

    Nope. This recursion comes from conditioning on what happens on the first roll. If on the first roll you roll more than (E-1) then your expectation is really (\frac{\lfloor E \rfloor +100}{2}) (you walk away after the first roll, and you haven't paid anything).
  53. pruse

    7.7 Jane Street Capital Second Round Interview

    Isn't the solution to that equation 87.25? The recursion we get for (E) if we want to maximize the e.v. is 1) (E = \frac{\lfloor E-1 \rfloor}{100}\cdot (E-1) + \large(1- \frac{\lfloor E-1 \rfloor}{100}\right)\cdot \frac{\lfloor E \rfloor +100}{2}), if ( E ) is not integral. The solution to...
  54. pruse

    job w/o programming skills?

    Welcome back to QN, Joy!
  55. pruse

    Job interviews: just don't do that!

    I don't get it.
  56. pruse

    Undergrad Math vs. Stats?

    Yeah, despite popular opinion, doing math will give you a strong foundation for a later (or concurrent) study of stats. You'll be stronger than most other applied math people who often only have a flimsy understanding of mathematics.
  57. pruse

    Level of math in a quant job

    Far from it.
  58. pruse

    Level of math in a quant job

    It works everywhere. Simplicity is efficiency, and nature is efficient.
  59. pruse

    Level of math in a quant job

    Most things in life are interesting. Complexity isn't a prerequisite. Occam's razor, baby.
  60. pruse

    Job interviews: just don't do that!

    Irony transcends culture.
  61. pruse

    QuantNet Campsite

    A hunting we will go, a hunting we will go Heigh ho, the dairy-o, a hunting we will go A hunting we will go, a hunting we will go We'll catch a fox and put him in a box And then we'll let him go A hunting we will go, a hunting we will go Heigh ho, the dairy-o, a hunting we will go A hunting we...
  62. pruse

    Job interviews: just don't do that!

    It never ceases to amaze how often 'smart' people miss irony and sarcasm.
  63. pruse

    Level of math in a quant job

    It's a different type of memory. And besides, the proportion of your typical mathematician's inability in chess that's attributable to their inability to understand other mindsets is probably significantly larger. I included lack of memory (particularly for interpersonal situations) as just one...
  64. pruse

    Level of math in a quant job

    Uhh, what was this thread about again?
  65. pruse

    Level of math in a quant job

    Eh, I am a quant for one of the BBs, and you know how many times I found myself exploiting the underlying math in order to make my code more efficient? In some cases computing time would have been 3x what it was had I not known the mathematical intricacies. Some of these things are subtle. And...
  66. pruse

    Level of math in a quant job

    The Chess vs. Math analogy doesn't quite apply to Programming vs. Math for the obvious reason that chess is a game. It requires foresight, putting yourself in the mind of another person, good memorization, etc. No wonder a lot of mathematicians are not good at chess -- for one, many have poor...
  67. pruse

    Level of math in a quant job

    DrD asked about quant roles, not developer roles. If you're just a developer, then you probably provide some kind of support to the quants, and don't always know all the mathematical details (but have some general idea of the structure). Quants though, do a bit of both. They do...
  68. pruse

    Level of math in a quant job

    Read my above post and read the part in parentheses about what being good at 'maths' means. I've never met a really good programmer who didn't also have good quantitative reasoning skills (which is what I mean by being good at 'math'). Also, every exceptional math person I've ever met has...
  69. pruse

    Level of math in a quant job

    With anything quant, yes of course.
  70. pruse

    Level of math in a quant job

    Hmm, don't listen to the above posts. Just because you'll be coding most of the time, does not mean that quant work isn't math. If you don't understand the mathematics of the thing you're coding, or if you don't know combinatorics, optimization, etc., you can't expect to be a good coder. A...
  71. pruse

    basic but tricky

    "It's sooo basic!"
  72. pruse

    Multinomial RNG

    Sorry, I had written it fast and made a couple of typos; I clarified things a bit. For the covariance matrix, you can get an estimate from a large number of samples.
  73. pruse

    Multinomial RNG

    This is a multivariate distribution, so you're actually generating vectors. 1. Randomly generate from one of (k) categories with probabilities (p_1,p_2,...,p_k). (This is easy enough. Generate a random number in [0,1], etc.) If category (j) is generated, produce the vector ((0,...0,1,0,...0))...
  74. pruse

    Useful Practice If You're Interested In Trading

    buy the rumor, sell the fact!
  75. pruse

    Where to buy a SUIT

    suit yourself!
  76. pruse

    IQ

    Plenty of people with half that IQ work in finance. Whoop-de-doo. At least the ones of higher IQ are keepin' it real...
  77. pruse

    IQ

    What good has that ever done her? Hmm, let's see: Vos Savant was Chief Financial Officer of Jarvik Heart, Inc. She has served on the Board of Directors of the National Council on Economic Education, on the advisory boards of the National Association for Gifted Children and the National...
  78. pruse

    IQ

    I'm a quant and mine was recently measured at a whopping 98.
  79. pruse

    Game of Thrones

    Obviously the two greatest shows of all time are Breaking Bad and The Wire. Obviously.
  80. pruse

    Is it relatively difficult to become an MD as a quant developer?

    Why would anyone care for a title? Why not instead care about being a good human being? Then the title might come. Not holding my breath though. ;)
  81. pruse

    What sports do quant play and what beers do quant drink?

    sports: handball (beating a bouncy blue ball against a wall; like tennis), tennis, some gymnastics, strength workouts (mostly calisthenics; there's so much to be done with just your body weight), and planning to get into parkour soon. beer: too many useless liquid carbs, defeats the above.
  82. pruse

    What sports do quant play and what beers do quant drink?

    Pears are most definitely the toughest. May Joy be in all of your hearts this Christmas season!
  83. pruse

    What sports do quant play and what beers do quant drink?

    Boxing what, oranges?
  84. pruse

    Will Columbia's Quant Certificate help me get into a top 10 MFE program?

    Columbia and Harvard are nothing more than names, they don't bring happiness in life :)
  85. pruse

    Taking balls from a box

    You're absolutely right. It's still true, though, that (P(X_1=1)=P(X_2=1)=\cdots=P(X_{99}=1)), by symmetry, so it should actually be (1+99\cdot\frac{50}{99}=51).
  86. pruse

    Best position in line

    indeedably it is! 'twas asked at JP Morgan.
  87. pruse

    Best position in line

    Let's find your probability of winning if you're in position (k) on line. For you to win, the people in positions (1,...,k-1) should all have distinct numbers, and you should have one of those numbers. The probability of this happening is...
  88. pruse

    Taking balls from a box

    (1) For the status number to be (K), the sequence of draws must have the form (A_1A_2...A_K), where each (A_i) is a homogeneous block of draws -- all white or all black -- and these blocks alternate in type. There must be (a=\lfloor \frac{K}{2} \rfloor) of one type of block and (b=K-\lfloor...
  89. pruse

    We don't need no education, No more thought control.

    We don't need no education, No more thought control.
  90. pruse

    Number of rounds

    Ha, are you serious? You were looking for a rigorous solution, and I set you up for one; the rest of it should be right-quick... We have to check the ratio of \(\binom{2k}{k}0.45^{k+1}0.55^{k}\) to \(\binom{2k-1}{k}0.45^k0.55^k\), which is easily computed as \(2\cdot 0.45 = 0.9<1\). This shows...
  91. pruse

    Choosing number game

    Yes, those should be 105's; that's what happens when you type fast. So you're saying that the sets \(\{1,2\}\) and \(\{3, 4, 5, ..., 20\}\) have equal probability? that's obviously not true; the first has the very small probability of \(\frac{1}{20}+\frac{1}{20}=\frac{2}{20}\), while the...
  92. pruse

    Where to buy a SUIT

    If you have the body type, go to Zara. You can get a nice fitted suit for $300-$400, plus it's Euro, so it's added style that you wouldn't get at an American place like Brooks Brothers where everyone shops. Worst thing is to wear baggy pants and look like a ninja; many people unfortunately are...
  93. pruse

    Problem on the job - bingo game

    Important note: A player can have only so many daubs before a bingo is reached. what does that mean exactly?
  94. pruse

    Number of rounds

    For \(n\) odd, you either win the last round, and you've come out at least even in the previous \(n-1\) rounds, or you lose the last round but you've come out on top in the previous \(n-1\): \( P_n = 0.55P_{n-1}+0.45 \large(...
  95. pruse

    Choosing number game

    Well, no, those two events are not equally likely to occur, unless those sets have the same size, which only occurs for \(x=10\). It's not about the probability of winning, so much as it is about the players' expected winnings. For instance, if player 1 plays 12, then player 2 will play 13...
  96. pruse

    Distance problem

    A poet; I like that. We need more of those around here!
  97. pruse

    Problem on the job - bingo game

    Well this is pretty convoluted, and I'm not sure what you're looking for. Can you be more precise? Also, i'm not familiar with Bingo. How does one get a bingo? And presumably, if the number of daubs can be bigger than 1, numbers may repeat within a given column?
  98. pruse

    Distance problem

    No, lobomattu actually has a point... vertical distance may be the same for the uphill and downhill parts, but the road distance may not. I guess you're supposed to assume the hills are symmetric, which is kind of silly. Let's just dismiss this as a bad problem :P
  99. pruse

    Choosing number game

    It's not that \(X\in\{1,...,x\}\) or \(X\in\{x+1,...,20\}\) if Player 1 picks \(x\) (\(X\) is random and can be anywhere)... it's that Player 1 knows what Player 2 will play after he plays \(x\) (see my argument above). Once he knows this, he knows what his expected winnings are because he knows...
  100. pruse

    Choosing number game

    \(E(winnings) = \sum_{k=1}^{20} E(winnings|X=k)P(X=k)=\sum_{k\in S}\frac{k}{20}\), where \(S\) is the set of \(X\)'s where you win (because for all other \(k\)'s, your winnings are 0). For instance, if you pick 11 and then your opponent picks 12, you of course win for any \(X\in \{1,...,11\}\)...
  101. pruse

    Distance problem

    The problem mentions that there are 'level' parts. In completing a full circuit, to go from level ground back to level, you must obviously go a total downhill distance equal to your total uphill distance.
  102. pruse

    Choosing number game

    No, it is 20 as I'm assuming the discrete case. And X is actually random from the point of view of the players: the point of view the problem is concerned with.
  103. pruse

    Choosing number game

    It's a two-part problem. (1) Figure out Player 2's optimal move for every move that Player 1 can make. (2) Figure out Player 1's optimal move based on what he knows Player 2 will do. This is all assuming each player is rational and seeks to maximize his expected winnings. Let \(f(x_1)\) be...
  104. pruse

    Choosing number game

    Maybe for him picking one unit higher or lower than me is not optimal. Either way, we should know what happens in the case where X is precisely in the middle of our picks.
  105. pruse

    Choosing number game

    What if we're equally close? X = 14, and we pick 12 and 16, say.
  106. pruse

    Choosing number game

    First off, is this discrete or continuous?
  107. pruse

    Distance problem

    Hehe. No problem.
  108. pruse

    Distance problem

    Whatever distance he goes uphill he must go downhill, so \(x/16+y/12+y/24 = 9/4\) \(3x+4y+2y = 108\) \(3x+6y = 108\) \(x+2y = 36\)
  109. pruse

    Pairwise Product Set Cardinality

    Can you justify that? (I don't think that's true.) Also, like Faisal, you are not using the fact that \(1\leq a_i\leq 2n+1\), which is crucial. This means that the argument is probably flawed.
  110. pruse

    7.7 Jane Street Interview Question...Needing Help

    Among the \(n\) noodles there are \(2n\) ends. Picking one end leaves \(2n-1\) other ends to match it with.
  111. pruse

    Expected number of tosses

    For each \(n\geq 1\), let \(X_n=1\) if there is no winner on the \(n\)-th toss. Then the expected number of tosses is \(1+\sum_{n=1}^\infty E(X_n)=1+\sum_{n=1}^\infty P(X_n=1)\). We'll show that \(P(X_n=1)=\frac{1}{2^n}\), so that the expectation evaluates to \(1+\frac{1}{2}+\frac{1}{2^2}+\cdots...
  112. pruse

    Choosing TT vs TH problem

    Yeah, that's already been established.
  113. pruse

    Choosing TT vs TH problem

    The probability of not getting any money doesn't tell the whole story, as it's possible for the cases that do make money to make disproportionately larger amounts. Your expected winnings, as well as the volatility of those winnings, are what matter. Now, between two alternatives with the same...
  114. pruse

    High school math competition as competitive sport

    I was captain of the Stuy math team and a member of the 2nd place ARML team in 2000. Ahh the high school days...
  115. pruse

    Choosing TT vs TH problem

    It ain't about googling, it's about sharing and discussing; I'm sure that's why tuanl posts his problems here. Use indicator variables: For each of the first \(n-1\) tosses, out of \(n\), let \(X_1=1\) if that toss and the next are TH, 0 otherwise. Then the expected number of TH's is equal to...
  116. pruse

    Ratio of two real numbers

    Because sign does not matter. The proportion of the first quadrant where the condition is fulfilled will therefore be the same as the proportion of the entire plane where the condition is fulfilled. It's \(\frac{2}{\pi}\) because we're dividing the total angle where the condition happens by the...
  117. pruse

    Ratio of two real numbers

    It's enough to treat the case \(a,b>0\). You need \(1\leq \frac{a}{b} \cdot 10^k <2\) for some integer \(k\), i.e., \(10^{-k} < \frac{a}{b} < 2\cdot 10^{-k}\). The region in the plane described by these inequalities is a windmill pattern of sectors in the first quadrant. The angles of these...
  118. pruse

    Counterfeit Coin problem

    Yes, it's 5. Now prove that it can't be done in 4...
  119. pruse

    Two interview questions

    You're right, I switched them. In other words, just reflect everything about the middle. 15 <-> 5. Thanks!
  120. pruse

    From a Goldman Sachs Quant interview

    you mean 999; one of them is surely poisoned.
  121. pruse

    Two interview questions

    It's even more basic. It's physically obvious: To balance an object on the left of a see-saw of length 20 with an object 3 times its weight on the right, the hinge must be placed 15 units from the left. But here's a mathematical proof for sticklers: If you guess \(a\), then your average...
  122. pruse

    Counterfeit Coin problem

    Yeah, I'm aware of the 12 coin problem. But your problem is 81 coins.
  123. pruse

    Pairwise Product Set Cardinality

    Okay, here's a correct proof. Let \(p < q < t < u\in \{n^2+1, ..., (n+1)^2\}\) such that \(pu = qt\). Note that \((u-p)^2 = (u+p)^2-4pu = (u+p)^2-4qt > (u+p)^2-(q+t)^2\), where the latter follows by the AM-GM inequality. Then \((u-p)^2>(u+p+q+t)(u+p-q-t)>4n^2(u+p-q-t)\). Note that since...
  124. pruse

    Pairwise Product Set Cardinality

    This is obviously wrong, since nowhere are you using the fact that a_1, a_2, b_1, b_2 are in the range [1,2n+1]...
  125. pruse

    Two interview questions

    For #2, Let \(S(t)\) and \(N(t)\) be the sum of the rolls, and the number of dice, respectively, in round \(t\). Then \(E(S(t)) = \frac{7}{2}N(t)\) \(E(N(t)) = \frac{4+5+6}{6}\cdot N(t-1) = \frac{5}{2}N(t-1)\) Taking expectations in the latter recursion and inducting...
  126. pruse

    Counterfeit Coin problem

    4 is most certainly wrong. You can do it in 4 only if you know that the counterfeit coin is, say, heavier.
  127. pruse

    Two interview questions

    Or you can just say: if they're all distinct, then their sum is \( \geq 1+2+\cdots+n=n(n+1)/2 \geq n\), a contradiction.
  128. pruse

    interview question

    This argument is lengthy, and might fool a lot of people, but unfortunately doesn't make any sense.
  129. pruse

    The State of Financial Engineering

    The article is genius -- serifed, bolded, and punctuated. It bashes incompetence with poetic glee. Talk about metacognition!
  130. pruse

    How good should a Quant be at Math?

    hmm... yeah, I think a quant should be pretty good at math.
  131. pruse

    Do american white people get affirmative action when applying to mfe programs?

    It's not about white vs. non-white, it's about who can actually communicate in English. you know, that part on your application where you check off your native language.
  132. pruse

    interview question

    Bump away.
  133. pruse

    interview question

    Besides, semantics aside, here is why 1 should be included among prime powers... When, for example, computing the number of factors of a number that we've prime-factorized, (p_1^{e_1}p_2^{e_2}\cdots p_k^{e_k}), every factor is of the form (p_1^{f_1}p_2^{f_2}\cdots p_k^{f_k}), where each (f_i)...
  134. pruse

    interview question

    Why are you still talking about prime powers? Did you not see that I rephrased the solution? Must be those bath salts again...
  135. pruse

    interview question

    Oh, sir, you're right, I humbly apologize for the misunderstanding. How could I ever think 1 was a power of a prime! But maybe we can still salvage ferdowsi's solution by rephrasing it... "Any perfect square that does not have more than 1 distinct prime factor."
  136. pruse

    interview question

    You've really gotta be kidding me. Of course 1 is a prime power: any prime to the zero. You really think they intended a solution as esoteric as "the basis set for representing positive integers with positive squares is " blah blah blah... ?? You must be high on bath salts.
  137. pruse

    interview question

    Why do you need 1 to be the square of a prime? If I define a set of numbers by the condition "...containing non-distinct prime factors," then the number 1 will vacuously satisfy this condition. Semantics, my friend, semantics. You can also take a more careful look at ferdowsi's statement...
  138. pruse

    interview question

    Of course ferdowsi 's solution works; think about it a tad bit more. His answer is much more likely to be the intended one and the one that I (most definitely!) agree with. Just consider bifunctional proportionality, followed by a little hedonic calculus, and you're good to go...
  139. pruse

    Stock Picking

    that's so... interesting...
  140. pruse

    improving rolls of a die

    You're right, of course. Thanks. :) Now, given how simple the final formula is, there has got to be a prettier solution...
  141. pruse

    improving rolls of a die

    The number of increasing sequences of elements of (\{1, ..., n\}) of length (k) and ending in (m) is (\binom{m-1}{k-1}) (pick the (k-1) elements less than (m) from (\{1, ..., m-1\}) and there's a unique way to order them). There are (m) ways in which the following roll won't improve on the last...
  142. pruse

    Santas at Christmas party

    haha, my algebra skills were way off here, you are right. i've fixed it.
  143. pruse

    See no evil, hear no evil, speak no evil...

    See no evil, hear no evil, speak no evil...
  144. pruse

    Santas at Christmas party

    Sure, but let's put an 's' at the end of Santa... this be a democracy of Santas.
  145. pruse

    Santas at Christmas party

    I get 100 too. Assume there are (n) santas at the party. There are (\frac{n(n-1)}{2}) potential relationships between them. Of these, (\frac{22n}{2} = 11n) are friendships. Therefore, (\frac{n(n-1)}{2}-11n) are non-friendships. For each non-friendship there are (6\cdot 2=12) friendships that...
  146. pruse

    Technical Interview for Quant Research Internship at J.P. Morgan

    it'll probably be brainteasers and tech questions, so read Heard On The Street and Frequently Asked Questions in Quantitative Finance.
  147. pruse

    How fast can you type?

    that's coo
  148. pruse

    NYC Drinks - QuantNet meet up?

    I'm goin' on tilt, all in!
  149. pruse

    Black Friday wishlist

    that's awesome
  150. pruse

    Probability Question

    Obviously that's incorrect... only if exactly half of all the bulbs are currently on can we say that the probability of one more on is the same as the probability of one more off. Trust me, the answer is about 21.75.
  151. pruse

    Probability Question

    so?
  152. pruse

    Black Friday wishlist

    Has anyone yet mentioned the Samsung UN55D7000L? Gotta love that narrow bezel!
  153. pruse

    Probability Question

    I saw this question and a bulb went off. The probability that a given bulb is on is the probability that it was flipped an odd number of times: (\binom{50}{1}0.02^10.98^{49}+\binom{50}{3}0.02^30.98^{47}+\cdots+\binom{50}{49}0.02^{49}0.98^1). This is equal to...
  154. pruse

    Help with simple math question

    1/2 - 1/2 + 1/6 1/4 - 1/3 + 1/8 1/6-1/4+1/10 1/8-1/5+1/12 1/10-1/6+1/14 ... Notice how terms cancel diagonally: (1/6+1/6-1/3), (1/8+1/8-1/4), ... the only term that survives is 1/4.
  155. pruse

    Sex discrimination in the finance industry

    It makes a lot of sense, and I suspect it's not really discrimination. Gaps in salary in general are larger in the financial sector. Everything is scaled up. So given that women's career goals and preferences are likely to be different, their salaries will be different.
  156. pruse

    How to display C++ code and math beautifully

    I've suggested this before... Writing math here would be a lot more fluid if it required typing only one character, like '$'.
  157. pruse

    "LongShort Hedge Fund" Toronto

    At least go get some free food.
  158. pruse

    crowing crows

    how is that? if 5 crows land on the number line at 0, 1, 3, 5, 6, then 3 isn't being crowed at, while the others are, including the end ones.
  159. pruse

    crowing crows

    The end crows each have probability 1/2 of not being crowed at. The penultimate crows on each end have 0 probability of not being crowed at. For each "interior" crow, the probability of not being crowed at is 1/4. So the expected number of crows that are not crowed at is...
  160. pruse

    Guess 3 natural numbers

    ha, but your solution is easier and probably the one they had in mind.
  161. pruse

    Guess 3 natural numbers

    It's really a combinatorics question at heart. For the first set of coefficients just pick (1,1,1). Whatever the result is, the number of possible triples (x,y,z) is finite -- they're constrained to the first octant because they're natural numbers, and only a finite number of lattice points on...
  162. pruse

    puzzle

    By AM-GM, the sum must be at least \(3\sqrt[3]{72}=12.48...\). But since they're integers, the sum must actually be at least 13. And as Tsotne shows, 13 is attainable.
  163. pruse

    7.7 Jane Street Interview Question...Needing Help

    1) Say there are (n) noodles in the bowl. Condition on whether the first knot results in a loop or just a longer noodle. The probability of the former is (\frac{1}{2n-1}) while the probability of the latter is (\frac{2n-2}{2n-1}). Denote by (E_n) the expected number of loops given (n) noodles...
  164. pruse

    The 25 Weirdest Interview Questions

    Yep, it's 2k-1 :) Now I guess you can generalize to (w) women, (k) condoms... Edit: Actually, a better formulation would be: Given (m) men and (w) women, what's the minimum number of condoms needed if each man fancies every woman?
  165. pruse

    The 25 Weirdest Interview Questions

    Even more than that.
  166. pruse

    The 25 Weirdest Interview Questions

    Nope. More.
  167. pruse

    The 25 Weirdest Interview Questions

    Given \(k\) condoms and one woman at their disposal, what is the greatest number of men that may have safe sex with the woman?
  168. pruse

    Probability of Discovering (N-1)st Point on a Circle

    You've gotta clarify some points (heheh) here... 1) Are the points numbered in order and we start at point #1? 2) Are you asking for the probability that the (N-2)-st distinct point to be hit is either r+1 or r-1?
  169. pruse

    2011-2012 Quantnet Ranking of Financial Engineering (MFE) Programs

    Why waste a breath on going "hmmm"? Clearly you go with the one that ranks you higher. If Joe ranks me #10 and Mike ranks me #1 I'm going with Mike, sorry.
  170. pruse

    2011-2012 Quantnet Ranking of Financial Engineering (MFE) Programs

    Conditional probabilities, people, conditional probabilities! All too often people forget to condition!
  171. pruse

    Gödel, Escher, Bach

    The Glass Bead Game... yes, absolutely, I second it!
  172. pruse

    Isn't this joke ambigious?

    does it really matter? there's obviously a typo; the real point of the joke is the irony at the end; end of story.
  173. pruse

    Hurricane Irene

    Wow, is your job really more important than your safety? Yes, man, hindsight *is* 20/20! And keep in mind that, even though your area may not have suffered much, some areas did get hit pretty hard!
  174. pruse

    Hurricane Irene

    What's with all the criticism? We're quants, not meteorologists. Better to be safe than sorry -- no?
  175. pruse

    SAT verbal question

    You can't just rearrange them like that. For one, that last sentence is a run-on sentence which either needs to be fixed by rephrasing or inserting some commas. Two, in a construction like "It weaves..., the Panama Canal linking..." It and the Panama Canal should be different entities, but the...
  176. pruse

    Anyone NYC member playing tennis?

    I play tennis! Who's down? I know some free courts up around 137th street, in Riverbank State Park. Also what I do if I can't make it to an actual tennis court is play against a handball wall; they're a lot easier to come by and the game can be just as fun and competitive. By the way, anyone...
  177. pruse

    Anyone else snag an HP touchpad for ~$100?

    Why is it trash? Which one do you have?
  178. pruse

    Anyone else snag an HP touchpad for ~$100?

    Any places still have 'em??
  179. pruse

    Which Quant Shops Hire Straight Out Of Undergrad?

    Well, between making millions on Wall Street and spending more time in school, which would you pick?
  180. pruse

    Which Quant Shops Hire Straight Out Of Undergrad?

    I know of a couple of such cases at DE Shaw; but they were a few years ago and the people were IMO gold medalists and Putnam Fellows. These places aren't gonna take your average Joe, especially not straight out of undergrad.
  181. pruse

    How to get around the city

    'cause those are real easy on ankles...
  182. pruse

    How to get around the city

    Hence the subway.
  183. pruse

    How to get around the city

    i also take the train from Penn. the quickest way is really by subway; take the N/R two stops.
  184. pruse

    Debt ceiling

    We need to accept the fact that some things are better left unsaid.
  185. pruse

    Need for needles

    Because I am talking about a volume (specifically, of the part of the sample space where the needles fall properly onto the stick); when you find volume you integrate 1 over the region. Then I divide this volume by the volume of the sample space, \((1-h)^n\). This is essentially equivalent to...
  186. pruse

    Need for needles

    Okay? And? You essentially repeated my solution...
  187. pruse

    It's 100°F plus degree in NYC today

    Very funny guys... since when do a couple of steaming hot days imply global warming? come on now. there is also evidence of cooling...
  188. pruse

    Fewer Perks and More Work for Wall St.’s Summer Interns

    I agree with Alexandre. When after a couple of years your health starts deteriorating because of the crap food you eat 'cause that's all they have in the kitchen down the hall, or you're in too much of a rush to eat a proper meal, and when you start to forget what it feels like to connect with...
  189. pruse

    It's 100°F plus degree in NYC today

    The weather is fantastic...
  190. pruse

    Fewer Perks and More Work for Wall St.’s Summer Interns

    The ridiculous hours people work in the big banks really make a person ask, "What's more important to me - a career, or a life?"
  191. pruse

    Apaharan

    no smiling? and what fun is that?
  192. pruse

    Apaharan

    3 Idiots is the best Bollywood movie I've ever seen. New York is also good but the acting in some parts is kind of bad.
  193. pruse

    The power of positive thinking

    It's not either/or. But I think you started this thread with a personal conception of what "positive thinking" is and you're not allowing for a broader definition. You seem to be defining positive thinking as a wholehearted but possibly blind belief in one's abilities. For instance, "overrating...
  194. pruse

    The power of positive thinking

    I agree, positive thinking is definitely good. And it's certainly better than negative thinking. But, positive thinking by itself won't cut it; it's awareness that matters more. Too many people are just not aware of their flaws and limitations. If they were maybe they could actually start...
  195. pruse

    NYC Drinks - QuantNet meet up?

    who's got which?
  196. pruse

    NYC Drinks - QuantNet meet up?

    the grades don't count, is what I meant, and they're canned as soon as the refresher is over. you only need to pass... better to take things easy; it's summer time, after all :]
  197. pruse

    NYC Drinks - QuantNet meet up?

    It's only the refresher, it doesn't even count...
  198. pruse

    NYC Drinks - QuantNet meet up?

    Near GCT is hardly a great place to go out. And besides, doing this near GCT only makes it convenient for some people, not others.
  199. pruse

    NYC Drinks - QuantNet meet up?

    As far as beer gardens go, the best I've been to is Studio Square in Astoria. It's a huge outdoor area with lots of tables and all sorts of specialty drinks and beer. Great place if the weather is good.
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