Question: Let W be a gamma random variable with parameters (t, Î²), and suppose that conditional on W = w, X1, X2, . . . ,Xn

Let W be a gamma random variable with parameters (t, Î²), and suppose that conditional on W = w, X1, X2, . . . ,Xn are independent exponential random variables with rate w. Show that the conditional distribution of W given that X1 = x1, X2 = x2, . . . ,Xn = xn is gamma with parameters

t + n,B + E x -1

Step by Step Solution

★★★★★

3.25 Rating (151 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Swx wxx fx ... View full answer

Question Has Been Solved by an Expert!

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

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

588-M-S-C-R-V (791).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

An insurance company supposes that each person has an accident parameter and that the yearly number of accidents of someone whose accident parameter is is Poisson distributed with mean . They also...

Verify that Var(X) = / 2 when X is a gamma random variable with parameters and .

Compute the hazard rate function of a gamma random variable with parameters (, ) and show it is increasing when 1 and decreasing when 1.

20. Let W be a gamma random variable with parameters (r, B), and suppose that conditional on W = w, X1, X2, , X, are independent exponential random variables with rate w. Show that the conditional...

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...

Math 350 - Homework 3 - Solutions 1. The bus will arrive at a time that is uniformly distributed between 8 and 8 : 30 A.M. If we arrive at 8 A.M., what is the probability that we will wait between 5...

STAT 400 G. Fellouris Fall 2015 Homework 10 Readings Sections 5.6, 5.7, 5.9 Sections 7.3-7.4 (pg. 326) Exercises 1. Sums of iid random variables are asymptotically normal Let X1 , . . . , Xn be...

Suppose we want to simulate a large number n of independent exponentials with rate 1call them X1,X2, . . . , Xn. If we were to employ the inverse transform technique we would require one logarithmic...

19. Suppose we want to simulate a large number n of independent exponentials with rate 1call them X1,X2, . . . ,Xn. If we were to employ the inverse transform technique we would require one...

For a company with a new product, how can you estimate its potential market share?

A construction company is considering changing its depreciation from the MACRS method to the historical SL method for a general purpose hauling truck. The cost basis of the truck is $100,000, and the...

In your own words, in using numbered/bullet point format, list the reasons a payer will reject a claim.

How is the adjoint matrix related to the cofactor matrix?

22. The random variables X and Y are said to have a bivariate normal distribution if their joint density function is given by $$f(x, y) = \frac{1}{2\pi\sigma_x\sigma_y\sqrt{1-ho^2}}$$ $$\times...

23. Suppose that F(x) is a cumulative distribution function. Show that (a) F(x) and (b) 1 - [1 - F(x)] n are also cumulative distribution functions when n is a positive integer. HINT: Let X 1 , . ....

24. Show that if n people are distributed at random along a road L miles long, then the probability that no 2 people are less than a distance of D miles apart is, when D L/(n - 1), [1 - (D/L)] n-1 ....

Those are my questions O. [172 Points] DETAILS PREVIOUS ANSWERS A boiler has four identical relief valves. The probability that any particular valve will open on demand is 0.93. Assume independent...

Estimating Mean SAT Math Score The SAT is the most widely used college admission exam. (Most community colleges do not require students to take this exam.) The mean SAT math score varies by state and...

When inputting an answer, round your answer to the nearest 2 decimal places (for VARIANCE round to 4 decimal places). If you need to use a calculated number for further calculations, DO NOT round...