Available Wednesday, Apr 25. Download now
Due May 2, 5pm
180 minutes (three hours)
8 questions. 3-4 on topics related to inference. Others on everything else
Honour code: No collaboration. No communication about the questions or your answers. Exams should be pledged and signed.
You may use three double-sided pages of notes
You should know the definitions of the following words/phrases. (You won’t need to regurgitate these definitions in an exam, but you’ll need them to understand the questions and solve the problems). Where possible, you should be able to express the phrase in both words and mathematics.
Give the mgf of a sum of independent random variables
Give the mgf of a sum of iid random variables
Compare and contast the law of large numbers to the central limit theorem.
Using the mgf, show that the mean of a sequence of iid normal rv’s is normally distributed
Using the clt, show the mean of a sequence of any iid rv’s is approximately normally distributed.
Give the distribution of the standard deviation of a sequence of iid normal random variables.
Describe the distribution of the standard deviation of a sequence of iid normal rv’s.
Use method of moments to find an estimator for a parameter
Use maximum likelihood to find an estimator for a parameter
Recall the five ways to connect an estimator with the true value and a distribution
Find a confidence interval for a mean, variance or simple function thereof.
Perform a hypothesis test.