HomeworkLib
Question

If X~Gamma(p/2, 2), Y~Gamma(q/2, 2) are independent with p > q, then what is the distribution...

If X~Gamma(p/2, 2), Y~Gamma(q/2, 2) are independent with p > q, then what is the distribution of Z = X - Y? Check all correct answers.

a. X2p/2-q/2

b. Gamma(p/2 - q/2, 2)

c. Gamma(p - q, 2)

d. X2p-q

math   Statistics-And-Probability   
0 0
Add a comment Improve this question Transcribed image text
Next > < Previous
Sort answers by oldest

Homework Answers

Answer #1

0 0
Add a comment
Know the answer?
Add Answer to:
If X~Gamma(p/2, 2), Y~Gamma(q/2, 2) are independent with p > q, then what is the distribution...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions

  • 7. Assume X gammala, y) and Y-gamma(8,7) are independent. (a) Show that U = X +...

    7. Assume X gammala, y) and Y-gamma(8,7) are independent. (a) Show that U = X + Y gamma(a +.). (b) Show that V = X/(X+Y) beta(a. 8). (c) Show that U and V are independent. (d) Show that W = 72 gamma(1/2, 1/2) if Z N (0,1).

  • 10) (11) Let X and Y be 2 independent random variables. Suppose X ~ Gamma(0, 38)...

    10) (11) Let X and Y be 2 independent random variables. Suppose X ~ Gamma(0, 38) and Y ~ Gamma(a, 2B). Let 2 = 2X +3Y. Determine the probability distribution of Z. (Hint: use the method of moment-generating functions

  • 1. Suppose X ∼ Gamma(a,b) and Y ∼ Gamma(c,d). Furthermore suppose X and Y are independent....

    1. Suppose X ∼ Gamma(a,b) and Y ∼ Gamma(c,d). Furthermore suppose X and Y are independent. Let W = X + Y . (a) Find the MGF of W. (b) What restrictions would need to be placed on the values of a, b, c, and d in order for W to be a Gamma Random Variable. What would the parameters be?

  • 2. LetX~Gamma(α = 2, β = 4), Y~Gamma(α = 3, β = 4), X & Y...

    2. LetX~Gamma(α = 2, β = 4), Y~Gamma(α = 3, β = 4), X & Y are independent, Z,-x+r, Z,-X + Y a) (3 pts) State the joint pdf oEX and Y. Simplify the expression, clearing all b) (9pts) Find the joint pdf of Z and Z, using the two variable transformation method. In addition, clearly write the support for this joint pdf. When done, your answer should include the expression Z1Z21,2)2048 2048 11 )24e-22/4 c) (5 pts) You should...

  • 12. Let X and Y be independent random variables, where X has a uniform distribution on the interval (0,1/2), and Y...

    12. Let X and Y be independent random variables, where X has a uniform distribution on the interval (0,1/2), and Y has an exponential distribution with parameter A= 1. (Remember to justify all of your answers.) (a) What is the joint distribution of X and Y? (b) What is P{(X > 0.25) U (Y> 0.25)}? nd (c) What is the conditional distribution of X, given that Y =3? ur worl mple with oumbers vour nal to complet the ovaluato all...

  • 12. Let X and Y be independent random variables, where X has a uniform distribution on...

    12. Let X and Y be independent random variables, where X has a uniform distribution on the interval (0,1/2), and Y has an exponential distribution with parameter = 1. (Remember to justify all of your answers.) (a) What is the joint distribution of X and Y? (b) What is P{(x > 0.25) U (Y > 0.25)}? (c) What is the conditional distribution of X. given that Y - 3? (d) What is Var(Y - E[2X] + 3)? (e) What is...

  • Suppose X and Y are independent and Prove the following a) U=X+Y~gamma(α + β,γ) b) V=X/(X...

    Suppose X and Y are independent and Prove the following a) U=X+Y~gamma(α + β,γ) b) V=X/(X + Y ) ∼ beta(α,β) c) U, V independent d) ~gamma(1/2, 1/2) when W~N(0,1) X ~ gammala, y) and Y ~ gamma(6, 7) We were unable to transcribe this image

  • LetX-Gamma(α = 2, β = 4), Y-Gamma(α = 3, β = 4), X & Y are...

    LetX-Gamma(α = 2, β = 4), Y-Gamma(α = 3, β = 4), X & Y are independent, Z,- , Z,-X + Y. X+Y a) (3 pts) State the joint pdf ofX and Y. Simplify the expression, clearing all Г's. b) (9 pts) Find the joint pdf of Zi and Z2, using the two variable transformation method. In addition, clearly write the support for this joint pdf. When done, your answer should include the expression c) (5 pts) You should see...

  • Having troubles with question 2. Please help 2. If X has a Gamma distribution with parameters...

    Having troubles with question 2. Please help 2. If X has a Gamma distribution with parameters a and B, then its mgf is given by (a) Obtain expressions for the moment-genérating functions of an exponential random variable and of a chi-square random variable by recognizing that these are special cases of a Gamma distribution and using the mgf given above. (b) Suppose that X1 is a Gamma variable with parameters α1 and β, X2 is a Gamma variable with parameters...

  • Question 1. The joint distribution of X and Y is given. Are X and Y independent?...

    Question 1. The joint distribution of X and Y is given. Are X and Y independent? fx.y(2, ) X/Y 1 2 3 0.06 0.42 0.12 2 0.04 0.28 0.08 Check all fx,y(2,y) = fx(x)fy(y), are they equal? What you can say about X and Y? Question 2. Consider the following joint PMF 2,y,z fx.y.z(2,y,) 100 1/4 1/4 010 1/4 1/4 001 1/4 1. Find the PMF of (X,Y). 2. Are (X,Y) independent?

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT