Question

Problem 4 True or False A Bookmark this page Instructions: Be very careful with the multiple choice questions below. Some are "choose all that apply," and many tests your knowledge of when particular statements apply As in the rest of this exam, only your last submission will count. 1 point possible (graded, results hidden) The likelihood ratio test is used to obtain a test with non-asymptotic level o True O False Submit You have used 0 of 3 attempts Save 1 point possible (graded, results hidden) The sample mean and the sample variance of i.i.d. random variables are always independent. True O False You have used 0 of 3 attempts Submit Save 1 point possible (graded, results hidden) Let U be a standard Gaussian random variable and V be a Х" random variable with d degrees of freedom. (No other assumptions are made about U and Vhen, vd is a Student t random variable with d degrees of freedom. ㄗ o True O False Save You have used 0 of 3 attempts Submit 1 point possible (graded, results hidden) Student's t test can be run even with a small sample size, as long as the data are i.i.d. Gaussian. O True O False Save SubmitYou have used 0 of 3 attempts 1 point possible (graded, results hidden) If X1,..., X are ii.d. random variables on a finite discrete sample space E, a x2 test can be run in order to test if the unknown distribution of X1 is uniform on E True False Save You have used 0 of 3 attempts Submit Multiple Choice Questions (cont.) A Bookmark this page 1 point possible (graded, results hidden) If Xi , . . . , Xn are i.id. random variables uniformly distributed on [0,0] for some unknown θ > 0, Wald's test can be used to test whether True O False You have used 0 of 3 attempts Submit Save 1 point possible (graded, results hidden) Let Xi, . . . , Xn X be n 1.1.d random variables. To test if they follow a Gaussian distribution, l'e·if their distribution belongs to the Gaussian family), you can use... (Check all that apply.) Note: Here, we are not testing whether X follows N (μ, σ*) for specific μ and σ2. We are testing whether there exists μ and σ2 such that X follows N (μ, σ2 ) Note (added May 1): The test is not required to be rigorous. The x goodness of fit test The Kolmogorov-Smirnov test O The Kolmogorov-Lilliefors test A normal QQ-test d 0 of 3 attempts You have use Save 1 point possible (graded, results hidden) Consider the model {R, {N (θ, 1)heR . Then the prior π (0) α 1 for all θ e R is called (check all that apply) D Improper O A Jeffreys prior None of the above SubmitYou have used 0 of 3 attempts Save 1 point possible (graded, results hidden) The maximum likelihood estimator is always unbiased. O True False Submit You have used 0 of 3 attempts Save

Answer 1

a) false

b) false

c) false

d) true

e) true

f) false

g) Ch square test

h) improper

i) false