Question

(9) Let X and Y be iid Exp(1) RV’s. Define U = X / (X+Y) and...

(9) Let X and Y be iid Exp(1) RV’s. Define U = X / (X+Y) and V = X + Y . Show your Work.

(a) Derive the joint density for (U, V ).

(b) What is the marginal distribution for U?

(c) Find the conditional mean E(X | V = 2).

(d) Are U and V independent? Explain why

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 U and V be two independent standard normal random variables, and let X = |U|...
Let U and V be two independent standard normal random variables, and let X = |U| and Y = |V|. Let R = Y/X and D = Y-X. (1) Find the joint density of (X,R) and that of (X,D). (2) Find the conditional density of X given R and of X given D. (3) Find the expectation of X given R and of X given D. (4) Find, in particular, the expectation of X given R = 1 and of...
Let X and Y be independent N(0,1) RVs. Suppose U = (X+Y)/squareroot(2) and V = (X-Y)/squareroot(2)....
Let X and Y be independent N(0,1) RVs. Suppose U = (X+Y)/squareroot(2) and V = (X-Y)/squareroot(2). Please derive the joint distribution of (U, V ) by using the Jacobian matrix method.
Suppose that X and Y are independent Uniform(0,1) random variables. And let U = X +...
Suppose that X and Y are independent Uniform(0,1) random variables. And let U = X + Y and V = Y . (a) Find the joint PDF of U and V (b) Find the marginal PDF of U.
Let X U (0, 1) and Y exp (1) be independent variables (v.a.’s) independent. What is...
Let X U (0, 1) and Y exp (1) be independent variables (v.a.’s) independent. What is the function probability density (f.d.p.) of the v.a. Z = X + Y?
4. Let X and Y be random variables having joint probability density function (pdf) f(x, y)...
4. Let X and Y be random variables having joint probability density function (pdf) f(x, y) = 4/7 (xy − y), 4 < x < 5 and 0 < y < 1 (a) Find the marginal density fY (y). (b) Show that the marginal density, fY (y), integrates to 1 (i.e., it is a density.) (c) Find fX|Y (x|y), the conditional density of X given Y = y. (d) Show that fX|Y (x|y) is actually a pdf (i.e., it integrates...
Consider the random variables X and Y with the following joint probability density function: fX,Y (x,...
Consider the random variables X and Y with the following joint probability density function: fX,Y (x, y) = xe-xe-y, x > 0, y > 0 (a) Suppose that U = X + Y and V = Y/X. Express X and Y in terms of U and V . (b) Find the joint PDF of U and V . (c) Find and identify the marginal PDF of U (d) Find the marginal PDF of V (e) Are U and V independent?
Let X and Y be two continuous random variables with joint probability density function f(x,y) =...
Let X and Y be two continuous random variables with joint probability density function f(x,y) = 6x 0<y<1, 0<x<y, 0 otherwise. a) Find the marginal density of Y . b) Are X and Y independent? c) Find the conditional density of X given Y = 1 /2
Let random variable X ∼ U(0, 1). Let Y = a + bX, where a and...
Let random variable X ∼ U(0, 1). Let Y = a + bX, where a and b are constants. (a) Find the distribution of Y . (b) Find the mean and variance of Y . (c) Find a and b so that Y ∼ U(−1, 1). (d) Explain how to find a function (transformation), r(), so that W = r(X) has an exponential distribution with pdf f(w) = e^ −w, w > 0.
Let X have an exponential distribution with mean of 1. Consider the transformation Y = exp(-X),...
Let X have an exponential distribution with mean of 1. Consider the transformation Y = exp(-X), and determine the density function of Y. a. y b. 1 c 1/y
Let X and Y have the joint p.d.f. f(x, y) = 1I(|x^2−y^2|<1). Then, (a) Find the...
Let X and Y have the joint p.d.f. f(x, y) = 1I(|x^2−y^2|<1). Then, (a) Find the marginal distributions of X and Y respectively. (b) Obtain the conditional distribution of Y given X=x,for 0< x <1. (c) Find the mean and variance of X only.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT