Question: Suppose that X 1 ,.......,X n is a random sample from a gamma distribution with parameters. Suppose that X1, . . . ,Xn is a

Suppose that X₁,.......,X_n is a random sample from a gamma distribution with parameters.

Suppose that X1, . . . ,Xn is a random sample from a gamma distribution with parameters a = 3 and 5. (a) Find the maximum likelihood estimator, B, of 5 and show that it is unbiased. (b) Use moment generating functions to show that B is a consistent estimator of [3. (c) Find the variance of B and show that it achieves the RaoiCramr lower bound for unbiased estimators of [3

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Suppose that X 1, ..., X n form a random sample from a distribution for which the pdf is as follows: Suppose also that the value of the parameter is unknown (>0) and that he prior distribution of is...

2. Let X1, ,X,,1 be a random sample from a Gamma distribution with parameters a and 6 = 9 1-in- Where a is known. Suppose the prior on r is gamma with parameters do and 60, Where (to and 60 are both...

stat 6509 at the university of memorial 3. Let X1, X2, . .. , Xn be a random sample from a gamma distribution with parameters a = 3 and 3 = 0 , an unknown parameter. Let X be the sample mean. a. Find...

please I just wrong answer so please if someone can help me with a correct answer 3. Let X1, X2, . .. , Xn be a random sample from a gamma distribution with parameters a = 3 and 3 = 0 , an unknown...

Let X1, X2, . . . , Xn be a random sample from a gamma distribution with known and with = 1/. Say has a prior pdf that is gamma with parameters 0 and 0, so that the prior mean is 00. (a) Find the...

1. Let X1, ..., X n be a random sample from a Poisson distribution with mean A. Let the prior distribution of 11 be gamma with parameters a: and 6, where a and 9 are known. a) Find the posterior...

Suppose that X1, ..., Xn is a random sample from a gamma distribution with parameters o and 3. (a) (3 points) If a = m, where m is a known integer, and S is unknown, find a pivotal quantity that has...

Hi, please see below my task and the answer I already got. My problem is that I do not understand the context and I still have a lot of question marks. Please explain the task, better to say the...

May I seek you help for the following questions about loss models application and probability, please? Thank you. Problem 1 (Required, 25 marks) (a) We let X be a non-negative continuous random...

Make up a numerical example to show why the Social Security tax is regressive.

Assume that you hold a portfolio that involves only positions in three mutual funds (A, B, and C): Mutual Fund A B C Assume that: The composition of these mutual funds is as follows: Mutual Fund Cash...

Directions: There is no separate specific instructor recording for this Discussion Assignment. It is fairly straightforward. See the learning objectives for the purpose of this assignment. It is a...

On June 13 , the board of directors of Siewert inc. declared a 5% stock dividend on its 120 million, $1 par, common shares, to be distributed on July 1. The market price of Siewert common stock was...