Solutions ASAP (15 points) Suppose XN(6.9)amd yN (o.)are independent noa random aab 6 and 0 are...
3. Let Ya» . . . , Yn be independent normally distributed random variables with E(X) Gai and V(X)-1. Recall that the normal density with mean μ and variance σ given by TO 202 (a) Find the maximum likelihood estimator β of β (b) Show that ß is unbiased. (c) Determine the distribution of β (d) Recall that the likelihood ratio test of Ho : θ 02] L1] L2] θ° is to θ0 against H1: θ reject Ho if L(e)...
1. (50 points) Suppose X1, ..., Xn form a random sample from a N(u,02) distribution with p.d.f. Fe 202, for – V2110 <x< . Assume that o = 2 is known. a) (10 points) Derive the 90% confidence interval for u that has the shortest length. You must show all details including the pivot you use. b) (8 points) Show that the sample mean is an efficient estimator for u. Assume in (c)- (f) that the prior distribution of u...
Suppose X1, .., Xn is a random sample from a N(0, a2) population, where variance o are known. Consider testing Ho : 0 = O0 vs. Hi 0 700 Q1(4pt): Using Likelihood Ratio Test (LRT) to obtain a level a test that rejects Ho if Уп(X — во) VП(х — во) <21-a/2 21-a/2 or о Q2(1pt): Is the two-sided test derived in 1) an uniformly most powerful test? If not, briefly state your reasons Q3 (1pt): Note that the test...
function: Suppose the random variable X has the following cunulative distribution 0 if-00<z<-8 0.1 if 8-6 0.71 if -1Kz<5 Parts (a) through (d) below will be hand-graded. See instructions in Question O of this assignment. a. Draw the cumulative distribution function. b. Find and draw the pmf of X. c. What is the expected value of X? Submit Answer Tries o/s d. What is the variance of X? Submit Answer Tries 0/5 e. What is P(X 2.5)? Submit Answer Tries...