Question: Let X1, ..., X, be i.i.d. Gamma(o, 8) distributed and a > 0 is known. The p.d.f. is f (E) = a-1 exp(-x/B), I >0.1.

Let X1, ..., X, be i.i.d. Gamma(o, 8) distributed and a > 0 is known. The p.d.f. is f (E) = a-1 exp(-x/B), I >0.1. Find the MLE of 8. (5 points) 2. Suppose we want to test Ho : 8 = Bo against H1 : 8 * Bo, for some known and fixed po >0. Develop a level a test for it, using the MLE as the test statistic. (15 points) 3. What is the power of your test at the point 81 # 8,? (5 points) You may use the fact that \\ X, ~ Gamma(no, B)

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!

The lifetime (in months) of a particular aircraft component follows a probability density function: f(x) = 0, x24 240 x3 , x>24 (a) A system contains 5 such independent components. What is the...

This is the picture of the question 1. (30 points) Let X1, .... X, be i.i.d. Normal(4, o?) random variables with common probability density function (pdf) 1 (r - 4)2 f(x 0) = - exp 0 >0. V2TO 202 (a)...

4. Maximum Likelihood Estimation Let X1, . . . , X... 6 Rd be 31 sample points drawn independently from a multivariate normal distribution N01, 2). (a) Suppose the normal distribution has an unknown...

1. A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die. Determine her...

Homework #1 (written-answer problems) 1. Suppose X1,..., X are i.i.d. with common PDF x(x) = \e\x for x 0 and \ > 0. Let X (1) ... n X (n) denote the order statistics of X1, ..., Xn. (a) Specify the...

ANSWER ALL QUESTIONS. BE SURE TO ANSWER 7.1.8. A balanced die is rolled 3 times. Let x1 be the number of times 1 appears and x2 be the number of times 2 appears. Work out the joint probability...

Please answer this question 1. (30 points) Let X1, .... Xn be i.i.d. Exponential(1/0) random variables with common probability density function (pdf) f(x|0) = exp (-), x>0, 0>0. (a) (8 points) Derive...

Probability and Statistics - Problem Set c Keith M. Chugg October 2, 2015 1 Preliminaries, Combinatorics, Set Probability 1.1. A number of bats are in a cave. 2 bats can see out of their left eye. 3...

11/26/2016 Fall 2016 Homework 12Due Thursday 12/1, before 8 PM. Must submit before 8PM. My sites / 16F-STATS100A-1 / HOMEWORK / Fall 2016- Homework 12-Due Thursday 12/1, before 8 PM. Must submit...

Table of z values and probabilities for the standard normal distribution. z is the first column plus the top row. Each cell shows P( X z). For example P( X 1.04) = .8508. For z

GIVE DETAILED EXPLANATIONS 11.2.1. Consider iid variables x1 ,... , xn distributed as uniform over [a, b], b > a. (1) Show that the largest order statistic is a consistent estimator for b; (2) Is the...

Kim works for Priority Packaging in Alberta and is paid $1,713.46 bi-weekly. She contributes 4% of her gross earnings to a Registered Retirement Savings Plan each pay. Kim pays $18.00 bi-weekly for...

S.I. unit of (a) Farad permittivity of free space is (b) Weber (c) CN-m (d) CNm

What does the WC stamped on the side of a DOT approved refrigerant recovery cylinder?

Quality Soft Drinks Ltd. wants to introduce the concept of statistical process control in the production department. Being a quality expert, you have been appointed by the company to coach the...