iid 20. Let X1, ...,Xn - Exp(a), the exponential distribution with failure rate 2. We showed...
iid 4. Let X1, ...,Xn Exp(a), the exponential distribution with failure rate 2. Show that the test which rejects the null hypothesis Ho :1= 1 in favor of the alternative Hj := 2 when <k for a fixed constant k > 0 is best of its size.
3. Let X1, ..., Xn, ... be iid random variables from the shifted exponential distribution: Se-(2-0) f( x0) = л VI (a) Find the MLE for 0. (b) Find the MLE for ø= EX. (c) Find the MOM estimator for 0.
2. Let X1, , Xn be iid exponential(9) random variables. Derive the LRT of Ho : ? = ?? versus Ha : ????. Determine an approximate critical value for a size-a test using the large sample approximation.
8.60-Modified: Let X1,...,Xn be i.i.d. from an exponential distribution with the density function a. Check the assumptions, and find the Fisher information I(T) b. Find CRLB c. Find sufficient statistic for τ. d. Show that t = X1 is unbiased, and use Rao-Blackwellization to construct MVUE for τ. e. Find the MLE of r. f. What is the exact sampling distribution of the MLE? g. Use the central limit theorem to find a normal approximation to the sampling distribution h....
8(100) Let X1,,Xn be iid from r(a, 6). (1)(50) Find the limiting distribution of the MLE of B. (2)(30) Find the limiting distribution of the MLE of B when a is known. (3)(20) Compare two asymptotic variances in (1) and (2), and make comment on it. 1ラ 8(100) Let X1,,Xn be iid from r(a, 6). (1)(50) Find the limiting distribution of the MLE of B. (2)(30) Find the limiting distribution of the MLE of B when a is known. (3)(20)...
4. Let X1, X2, ..., Xn be iid from the Bernoulli distribution with common probability mass function Px(x) = p*(1 – p)1-x for x = 0,1, and 0 < p < 1 14 a. (4) Find the MLE Ôule of p.
Let X1, X2, ...... Xn be a random sample of size n from EXP() distribution , , zero , elsewhere. Given, mean of distribution and variances and mgf a) Show that the mle for is . Is a consistent estimator for ? b)Show that Fisher information . Is mle of an efficiency estimator for ? why or why not? Justify your answer. c) what is the mle estimator of ? Is the mle of a consistent estimator for ? d) Is...
Q6: Let X1, ..., Xn be a random sample of size n from an exponential distribution, Xi ~ EXP(1,n). A test of Ho : n = no versus Hain > no is desired, based on X1:n. (a) Find a critical region of size a of the form {X1:n > c}. (b) Derive the power function for the test of (a).
1. Let x1, ..., xn be a random sample from the exponential distribution f(x) = (1 / theta)e^(-x / theta) for x > 0. (a) Find the mle of theta ## can use R code (b) Find the Fisher information I(theta) ## can use R code
Let X1, X2,...,Xn be a random sample from the exponential distribution with rate A Let c > 0 be a fixed and known number. For i 1,2 п, let ..1 -{: : if Xic 1 Y otherwise Suppose that you get to observe Yı, Y2,... , Y,n but you do not get to observe X1, X2,... , X,n п. Find the MLE for X based on this information