5/5 Monday
We had a review session in class.
The final exam is scheduled on 5/15 Thursday 10:15-12:15 pm. Final exam will be cumulative, and I recommend you going over all homework problems and make sure you can do those by yourself.
5/1 Thursday
We covered the large deviation principle.
4/29 Tuesday
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4/28 Monday
We covered the sample mean and sample variance, and discussed the sampling distribution.
Office hour today (4/28 Monday) is canceled as I have to attend a meeting.
4/24 Thursday
We proved the Strong Law of Large Numbers.
4/21 Monday
In this week, we will be working on proving the law of (strong) large numbers. Here is a note for the proof. Please read the proof in advance and understand it as much as you can.
4/17 Thursday
We went over some questions from Homework 11.
I made some mistake when I did the number 3. Var(X)=E[Var(X|N)] + Var(E[X|N]). Since E[Var(X|N)]=E[Np(1-p)]=λp(1-p) and Var(E[X|N])=Var(Np)=λp^2 (in class, I mistakenly said it is λp instead of λp^2). Hence, Var(X)=E[Var(X|N)] + Var(E[X|N])=λp(1-p)+λp^2=λp. Hence, Cor(X,N)=\sqrt{p} (square root of p).
4/14 Monday
We covered covariance and correlation.
4/10 Thursday
We covered the order statistics.
4/7 Monday
We covered the moment generating functions.
4/3 Thursday
We covered the conditional expectation.
3/31 Monday
We covered the conditional distribution for discrete random variables.
3/27 Thursday
We covered the conditional distribution for discrete random variables.
3/24 Monday
We covered the convolution method.
3/23 Sunday
Homework 8 is posted and it is due 3/31 Monday.
3/13 Thursday
We took Midterm in class.
Have a wonderful Spring Break.
3/10 Monday
We continued our discussion on 2.4 Change of Variable Method.
We will take Midterm this Thursday 3/13 in class.
3/6 Thursday
We covered Section 2.3 Cumulative Distribution Method and 2.4 Change of Variable Method. Homework 7 is due 3/10 Monday.
We postponed Midterm to 3/13 Thursday.
3/3 Monday
We covered Section 2.2 Joint Distributions and Independence.
We postponed Midterm to 3/13 Thursday.
Chapter 2 of our lecture note is updated with more sections added.
2/27 Thursday
We covered Section 2.1 Joint and Marginal Density Functions.
2/24 Monday
We proved the Stirling formula and use this to prove the Central Limit Theorem for binomial distributions.
2/20 Thursday
We covered the normal distribution.
2/17 Monday
We covered Uniform Distribution and Exponential and Gamma Distributions.
2/13 Thursday
We covered the negative binomial distribution. Homework 4 is due next Monday.
2/10 Monday
We covered Geometric distribution. Here is an incomplete lecture note from the previous semester. Please use it only for your study purpose and do not circulate or post it online.
In case our class is canceled due to inclement weather this Thursday 2/13, homework 4 will be postponed to 2/20 Thursday (otherwise, it is due next Monday 2/17).
2/6 Thursday
We covered the Poisson distribution. Please bring your labtop to class on 2/10 Monday. We will be working on R/RStudio in class.
Here is a YouTube video for the overbooking problem. Please watch it.
2/3 Monday
We covered the Binomial Distribution. Homework 2 solution is posted.
1/30 Thursday
We discussed random variables, their probability mass function and probability density function, cumulative distribution functions, expectation, and variance.
1/27 Monday
We covered Sample space, events, and probability measure. Homework 2 is posted and is due next Monday.
1/23 Thursday
This is the first day of class and we went over syllabus and introduced R/RStudio and what we can do with them. Please download R and RStudio in your personal computer or find labs with it. Homework 1 is due 1/27 Monday by the start of the class.
1/20 Monday
Welcome to MAT 493 Mathematical Statistics. I will make announcements here after every class, so please check here often.
Homework 11 due 4/21 Monday, Solution
Homework 10 due 4/14 Monday, Solution
Homework 9 due 4/7 Monday, Solution
Homework 8 due 3/31 Monday, Solution
Homework 7 due 3/10 Monday, Solution
Homework 6 due 3/3 Monday, Solution
Homework 5 due 2/24 Monday, Solution
Homework 4 due 2/17 Monday, Solution
Homework 3 due 2/10 Monday, Solution
Homework 2 due 2/3 Monday, Solution
Homework 1 due 1/27 Monday by the start of the class