Statistics 100C Homework 1 Exercises

| August 30, 2017

Question
Exercise 6 Consider the regression model yi = ?0 + ?1xi + i . Find cov(ei , ej ).

Exercise 7 Suppose Yi = ?xi + i . In this equation X is non-random, ? is a parameter (unknown), and ? N(0, ?). a. Find the mean of Y . b. Find the variance of Y . c. What distribution does Y follow? d. Write down the likelihood function based on n observations of Y and x. e. Find the maximum likelihood estimate of ?. Denote it with ?ˆ. f. Show that the estimate of part (e) is unbiased estimator of ?. g. Find the variance of this estimate.

Exercise 8 Consider the model of exercise 7. Find the covariance between ei and ej . Also find the variance of ei .

Get a 30 % discount on an order above $ 100
Use the following coupon code:
RESEARCH
Order your essay today and save 30% with the discount code: RESEARCHOrder Now
Positive SSL