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Probability Theory

Joined
3/13/12
Messages
24
Points
13
I'm wondering why my school does not have a course regarding Probability Theory... I'm looking at these course descriptions and cannot find even a similar course named "differently". Can someone please list maybe 3 important concepts learned in probability theory? thanks
 
Just look at the required course list for statistics majors. You should find an equivalent to probability theory.
 
Joint Distributions, CDF, PDF, etc...

Usualy Stats 101 covers a lot that is in Prob Theory; do you need the course name or the material? (Are you trying to apply to a program that requires it?)
 
During my undergrad all the above things mentioned were covered in an introductory level Probability and Statistics course.Probability Theory was mostly about Borel Sets,Measure Space,Convergence Theorems.If you want i can paste the whole syllabus here.
 
Thank you all for quick responses :)

I was trapped in thinking that the probability theory (being rigorous) should be 3rd or 4th year course.

Based on the concepts mentioned above, I think the closest one that matches is "Introduction to Statistics II", which is a 2nd year course.

Course description goes:

This course provides students with an introduction to statistical methods with an emphasis on applications using continuous probability models.
This course serves as an introduction to mathematical statistics, and is devoted to the study of the basic probability tools needed in the theory of statistical inference. Topics include joint distributions, multivariate change of variables formula, conditional and marginal distributions, conditional expectation, covariance and correlation, and moment generating functions. Distributional results including those associated with normally distributed observations are examined. In addition, this course considers maximum likelihood and Bayesian estimation (time permitting). The topics considered in this course require knowledge of univariate and multivariate calculus.
 
Actually its true, Probability Theory course was a 3rd year course at least at my university and rigorous too,I can't say how it is at other universities.
In my opinion,the course you have mentioned is not really a Probability Theory course but as name suggests another Statistics course.If you haven't learned all those things yet which are mentioned in the syllabus of the above course then you should first take this course.
 
Thank you Shantanu Kumar,

However, I find no other upper year "undergraduate" course in "Statistics Honours Major" that deals with probability theory at a higher level.

Except: There are courses such as Mathematical Statistics I, and Mathematical Statistics II. Are these very closely related to Probability Theory that people mention on this website and on MFE websites?

Measure theory is offered as a graduate course, which requires real analysis knowledge.
 
konadian - you mentioned in a previous thread that you attend a Canadian university. The description of Introduction to Statistics II sounds familiar - almost identical to a course I took. Which school are you attending if you don't mind me asking?
 
Thank you all for quick responses :)

I was trapped in thinking that the probability theory (being rigorous) should be 3rd or 4th year course.

Based on the concepts mentioned above, I think the closest one that matches is "Introduction to Statistics II", which is a 2nd year course.

Course description goes:

This course provides students with an introduction to statistical methods with an emphasis on applications using continuous probability models.
This course serves as an introduction to mathematical statistics, and is devoted to the study of the basic probability tools needed in the theory of statistical inference. Topics include joint distributions, multivariate change of variables formula, conditional and marginal distributions, conditional expectation, covariance and correlation, and moment generating functions. Distributional results including those associated with normally distributed observations are examined. In addition, this course considers maximum likelihood and Bayesian estimation (time permitting). The topics considered in this course require knowledge of univariate and multivariate calculus.
sounds about right
 
These courses are generally perquisite for Probability Theory courses.So yes they are related.But then i am not sure how much Probability is required during MFE admissions as i never applied for one.
Ken clarified it.
 
Course description goes:

This course provides students with an introduction to statistical methods with an emphasis on applications using continuous probability models.
This course serves as an introduction to mathematical statistics, and is devoted to the study of the basic probability tools needed in the theory of statistical inference. Topics include joint distributions, multivariate change of variables formula, conditional and marginal distributions, conditional expectation, covariance and correlation, and moment generating functions. Distributional results including those associated with normally distributed observations are examined. In addition, this course considers maximum likelihood and Bayesian estimation (time permitting). The topics considered in this course require knowledge of univariate and multivariate calculus.

Pick up and read a basic text in probability if you haven't already taken a first course. The course description above seems to assume a first course.
 
Same here.

There's a course called Elementary Probability which covers probability spaces, conditional probability, distributions functions, moment generating functions and limit theorems. MATH 2030 - a second year course. This is a prerequisite for MATH 2131, which is an extension of 2030 to a multivariate setting.

I've taken both of these in addition to Mathematical Stats I and II. Feel free to PM me if you have any questions.

For upper year undergrad courses in probability, you might want to consider MATH 4430/4431 which are offered in alternating years.
 
These courses are generally perquisite for Probability Theory courses.So yes they are related.But then i am not sure how much Probability is required during MFE admissions as i never applied for one.
Ken clarified it.
Hmmmm. That material was part of my Probability Theory course, not part of a prerequisite.. Maybe they just dumb-down the material at American universities. I took it as part of my MS, but I shared the basic courses (probability, inference, multivariate) with the Ph. Ds.
 
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