Recent content by quantyst

I just discovered a serious conceptual but subtle error in my solution. In one of the steps in my approach I've assumed something that's not the case. Quite a learning experience! I will need to spend some time correcting my approach. I will probably come back to admit other errors. I just...

Thank you for the good work. Just one request. Can you please show me the algorithm used in your code so that I can better relate to your code? Thank you for your response.

You wrote above that: "so that the second roll is now treated as the initial roll". This means that you are actually ignoring the very first roll of the ENTIRE game. But you cannot do that as we must look at the TOTAL sum of the ENTIRE game. If the first roll is, say, five and the second roll...

Let's have two 'parallel' but uncommingled arguments going on, if you don't mind. So, please do not mingle this post (or SUB-THREAD) with the one we have been having so far. Let's call this sub-thread the quantyst's approach. Would you please just tell me where I went wrong with my solution...

I am puzzled as to how you are so certain of your attributions onto me when you write: "you [meaning I] assumed that the third roll is Roll1 and the fourth one is Roll2". I've done no such thing. Let's be concrete about this. Suppose the first roll of the entire game is 5 and the second roll...

Dear AlexandreH, Thank you for your response which I read completely. It is apparent, and I will show it to you if only you read and honestly try to understand my response, that you've missed the sequence of events here. First off, let's begin with peterruse's last step when he writes...

Dear Rados Radoicic, Please stick with the subject matter at hand. I would rather finish one thing at a time rather than mix many unrelated things together in one post. If you want to do a thorough analysis of my exchanges with peterruse, I'd be glad to do it later. So, on to your claim that...

Please stick with the subject at hand. Please do not evade the main issue. I have pinpointed EXACTLY where you went wrong with your solution. Please be a gentleman and take a look at what I said regarding your error.

You are funny. Again you are reverberating with your classic fallacy. You hardly read people's posts even when they show where you went wrong.

The underlined above is actually incorrect! You forget that by this time you actually have two different odd rolls, whose sum is even, and it is the parity of the sum that matters here regardless of what the actual number are.

You are committing a classic fallacy. You say that because my method and answer are different from yours, then my answer must be wrong. By your own logic, why shouldn't your answer be wrong precisely because it is different from mine? So, what's the resolution here? How do we go about...

Answer: Probability of Sum being Even is 4/7 and Probability of Sum Being Odd is 3/7. Here's why: Let p denote the probability of the sum being even when the game stops. Upon the first throw, we have Case (O) an odd roll with probability 1/2, and Case (E) an even roll with probability 1/2...

Here's a solution: Obviously for y<0: f(y)=0. For 0<=y<=1: f(y)=exp(y)=e^y. For 1<y: f(y)= 1 + INTEGRAL{f(u) [where u runs from (y-1) to y]}, which upon differentiation, gives f'(y)=f(y)-f(y-1). Now we can partition the interval [1,infinity) as [1,2)U[2,3)U[3,4)U...U[n,n+1)U.... so that for...

Nice problem. I'd like to generalize it as follows: Let X(1), X(2), ... be independent and identically distributed uniform random variables over [0,1]. Let y be any real number. Set N(y)=min{n: X(1)+X(2)+...+X(n)>y}. Find expected value E[N(y)]. As has been shown, E[N(1)]=e. If we let...

Interview (Thirty minutes) 1) Suppose you are given the opportunity to bid for a treasure chest, which you know with 100% confidence to be priced anywhere between $0-$1000. If you bid equal to or above the price, you win the treasure chest (at the cost of your bid). If you bid below the...