Question

Let X1, X2 be a sample of size 2 from the Gamma (Alpha=2, Lamba = 1/theta)...

Let X1, X2 be a sample of size 2 from the Gamma (Alpha=2, Lamba = 1/theta) distribution

X1 = Gamma = x/(theta^2) e^(-x/theta)

Derive the joint pdf of Y1=X1 and Y2 = X1+X2

Derive the conditional pdf of Y1 given Y2=y2. Can you name that conditional distribution? It might not have name

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
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
Similar Questions
Let X1 and X2 be independent random variables with joint pdf f(x1, x2) =x1e^−(x1+x2), 0< x1<∞,...
Let X1 and X2 be independent random variables with joint pdf f(x1, x2) =x1e^−(x1+x2), 0< x1<∞, 0< x2<∞. Y1= 2X1 and Y2=X2−X1. I) Find g(y1, y2), the joint pdf of Y1, Y2 Include and draw the support. II) Find g1(y1), the marginal pdf of Y1. III) Find E(Y1).
Let f(x1, x2) = 1 , 0 ≤ x1 ≤ 1 , 0 ≤ x2 ≤...
Let f(x1, x2) = 1 , 0 ≤ x1 ≤ 1 , 0 ≤ x2 ≤ 1 be the joint pdf of X1 and X2 . Y1 = X1 + X2 and Y2 = X2 . (a) E(Y1) . (b) Var(Y1) (c) Consider the marginal pdf of Y1 , g(y1) . What is value of g(y1) where y1 = 1/3 and y1 = 6/4 ?
Let X1 and X2 be a sample from a uniform distribution on [0, 1] and let...
Let X1 and X2 be a sample from a uniform distribution on [0, 1] and let Y1 = min{X1, X2}, Y2 = max{X1, X2}. Find fY1 (y1|Y2 = y2). A. 1/ 2 B. 1 / 2y2 C. 1 /y2 D. 2 E. 1
1. Let x ∼ Np(µ, Σ). (1) Find the distribution of xp conditional on x1, ....
1. Let x ∼ Np(µ, Σ). (1) Find the distribution of xp conditional on x1, . . . , xp−1. (2) Suppose Σ =(1 ρ ρ 1 )and let y1 = x1 + x2 and y2 = −x1 + x2. Determine the joint distribution of y1 and y2. (3) Suppose Σ =( σ11 σ12 σ21 σ22 )and define y1 and y2 as in part (2).Determine the joint distribution of y1 and y2. Determine the conditional distribution y2 given y1.
Suppose that X1 and X2 denote a random sample of size 2 from a gamma distribution,...
Suppose that X1 and X2 denote a random sample of size 2 from a gamma distribution, Xi ~ GAM(2, 1/2). Find the pdf of W = (X1/X2). Use the moment generating function technique.
Let X1, … , Xn. be a random sample from gamma (2, theta), where theta is...
Let X1, … , Xn. be a random sample from gamma (2, theta), where theta is unknown. Construct a 100(1 - a)% confidence interval for theta. As a pivot r.v. consider 2 (n∑i=1) (Xi / theta)      NOTE: gamma (2, theta) = gamma (a, b), where a = 2 and b = theta.
5. Let a random sample, X1, X2, ..., Xn of size n = 10 from a...
5. Let a random sample, X1, X2, ..., Xn of size n = 10 from a distribution that is N(μ1, σ2 ) give ̄x = 4.8 and s 2+ 1 = 8.64 and a random sample, Y1, Y2, ..., Yn of size n = 10 from a distribution that is N(μ2, σ2 ) give y ̄ = 5.6 and s 2 2 = 7.88. Find a 95% confidence interval for μ1 − μ2.
Let (X1, X2) have joint pdf f(x1, x2) = (2/9)x1x22, 0 <= x1 <= 1, 0...
Let (X1, X2) have joint pdf f(x1, x2) = (2/9)x1x22, 0 <= x1 <= 1, 0 <= x2 <= 3 (i) What is the distribution of Y = X1 + X2? (ii) What is the distribution of Y = X1 * X2? (iii) Find the expectation E(X1 + X2) (iv) Find the expectation E(X1X2)
If X1 and X2 denote random sample of size 2 from Poisson distribution, Xi is distributed...
If X1 and X2 denote random sample of size 2 from Poisson distribution, Xi is distributed as Poisson(lambda), find pdf of Y=X1+X2. Derive the moment generating function (MGF) of Y as the product of the MGFs of the Xs.
1. An electronic system has two different types of components in joint operation. Let X1 and...
1. An electronic system has two different types of components in joint operation. Let X1 and X2 denote the Random Length of life in hundreds of hours of the components of Type I and Type II (Type 1 and Type 2), respectively. Suppose that the joint probability density function (pdf) is given by f(x1, x2) = { (1/8)y1 e^-(x1 + x2)/2, x1 > 0, x2 > 0 0 Otherwise. a.) Show that X1 and X2 are independent. b.) Find E(Y1+Y2)...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT