Question: Let W be a gamma random variable (, ), and let Y be an exponential random variable of parameter W. Find the marginal density of

Let W be a gamma random variable (, ), and let Y be an exponential random variable of parameter W. Find the marginal density of Y and the conditional density of W given Y = y.

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!

10.2.1. If x are iid from a uniform population over [0, 1], evaluate the density of x1 + + xn for (1) n = 2; (2) n = 3. What is the distribution in the general case? 10.2.2. If x1 ,... , xn are iid...

only do 12 (1) The probability that an "accident prone" policy holder has an accident within a year is 0.6, while the probability that a "non-accident prone" policyholder has an accident within a...

Only do(7)(8) (1) The probability that an "accident prone" policy holder has an accident within a year is 0.6, while the probability that a "non-accident prone" policyholder has an accident within a...

Only do (9)(10) (1) The probability that an "accident prone" policy holder has an accident within a year is 0.6, while the probability that a "non-accident prone" policyholder has an accident within...

(a) Let X be a continuous random variable representing the time to failure of a computer with the probability density function: f(x) -{3 0 Ikea 20 *

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...

Problem 3: Let W,..., Wz be a random sample from an Exponential distribution with density f(w\B) = Bexp (-w) for w > 0, with >0, and let Z be a zero-truncated Poisson random variable with p.d.f....

7:12 PM P P . D .Ill 11 3011 84 25 111 1618253302216_Sta... . . . A type of network router has a bandwidth total to first hardware failure called S expressed in terabytes. The random variable S is...

Please help me with Question three and four 7:12 PM P P . D .Ill 11 3011 84 25 111 1618253302216_Sta... . . . A type of network router has a bandwidth total to first hardware failure called S...

2. Let X1,X2, be a stream of random variables such that X1 is Poisson distributed with mean and, conditional on (X1,,Xj),Xj+1 is Poisson distributed with mean +1{Xj>0}, for j=1,2,, where 1\{\}}...

Propose a structure for compound E, C7H12O2, which has the following 13C NMR spectral data: Compound E Broadband-decoupled 13C NMR: 19.1, 28.0, 70.5, 129.0, 129.8, 165.8 DEPT-90: 28.0, 129.8 ...

You wish to purchase a $1,000 bond from a friend who needs the money. There are 7 years remaining until the bond matures, and interest payments are quarterly. You decide to offer $750.08 for the bond...

What are the advantages and disadvantages of stock repurchases? Are there any risks? What are some of the reasons that a company considers stock repurchase? Provide examples.

SW2H is a process Improvement technique asking questions about a process that can lead to cost and waste reduction, Sw2H stands for? What is done and How it is done What? Why? Where? When? Who? How?...

Cushing Medical Clinic operates a cardiology care unit and a maternity care unit. Ned Carson, the clinics administrator, is investigating the charges assigned to cardiology patients. Currently, all...

Autotech Manufacturing is engaged in the production of replacement parts for automobiles. One plant specializes in the production of two parts: Part #127 and Part #234. Part #127 produced the highest...

Refer to the data given in Problem 4-30 and suppose that the expected activity costs are reported as follows (all other data remain the same): Required: 1. Determine the percentage of total costs...