Question

Let X and Y be independent random variables, with X following uniform distribution in the interval...

Let X and Y be independent random variables, with X following uniform distribution in the interval (0, 1) and Y has an Exp (1) distribution.

a) Determine the joint distribution of Z = X + Y and Y.

b) Determine the marginal distribution of Z.

c) Can we say that Z and Y are independent? Good

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
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 and Y independent random variables with U distribution (−1,1). Using the Jacobian method, determine...
Let X and Y independent random variables with U distribution (−1,1). Using the Jacobian method, determine the joint distribution of Z=X-Y and W= X+Y.
Let X and Y be independent random variables each having the uniform distribution on [0, 1]....
Let X and Y be independent random variables each having the uniform distribution on [0, 1]. (1)Find the conditional densities of X and Y given that X > Y . (2)Find E(X|X>Y) and E(Y|X>Y) .
(a) Given two independent uniform random variables X, Y in the interval (−1, 1), find E...
(a) Given two independent uniform random variables X, Y in the interval (−1, 1), find E |X − Y |. (b) Let X, Y be as in (a). Find the support and density of the random variable Z = |X − Y |. (c) From (b), compute the mean of Z and check whether you get the same answer as in (a)
Let ? and ? be two independent random variables with uniform distribution. ?(? = 0|? =...
Let ? and ? be two independent random variables with uniform distribution. ?(? = 0|? = ?, ? = ?) = 1 − ?, ?(? = 1|? = ?, ? = ?) = ?(1 − ?) and ?(? = 2|? = ?, ? = ?) = ??. 1. Find the conditional joint p.d.f. (the posterior) ??,?|?=?. 2.Write down the conditional expectation ?[?|? = ?] and ?[?|? = ?] as functions of ?.
Let LaTeX: X,YX , Y be two discrete random variables that have the following joint distribution:...
Let LaTeX: X,YX , Y be two discrete random variables that have the following joint distribution: x = 0   1 y = -1   0.18   0.12 0   ?   0.20 1   0.12   0.08 (a) Determine the following probabilities: LaTeX: P(X=0, Y=0) P ( X = 0 , Y = 0 ), LaTeX: P(X\le 0,Y\le 0)P ( X ≤ 0 , Y ≤ 0 ) (b) Find the marginal distribution of LaTeX: YY. (c) What is the conditional distribution of LaTeX: XX given...
The random variables X and Y are independent. X has a Uniform distribution on [0, 5],...
The random variables X and Y are independent. X has a Uniform distribution on [0, 5], while Y has an Exponential distribution with parameter λ = 2. Define W = X + Y. A.    What is the expected value of W? B.    What is the standard deviation of W? C.    Determine the pdf of W.  For full credit, you need to write out the integral(s) with the correct limits of integration. Do not bother to calculate the integrals.
Let U1 and U2 be independent Uniform(0, 1) random variables and let Y = U1U2. (a)...
Let U1 and U2 be independent Uniform(0, 1) random variables and let Y = U1U2. (a) Write down the joint pdf of U1 and U2. (b) Find the cdf of Y by obtaining an expression for FY (y) = P(Y ≤ y) = P(U1U2 ≤ y) for all y. (c) Find the pdf of Y by taking the derivative of FY (y) with respect to y (d) Let X = U2 and find the joint pdf of the rv pair...
2.33 X and Y are independent zero mean Gaussian random variables with variances sigma^2 x, and...
2.33 X and Y are independent zero mean Gaussian random variables with variances sigma^2 x, and sigma^2 y. Let Z = 1/2(X + Y) and W =1/2 (X - Y) a. Find the joint pdf fz, w(z, w). b. Find the marginal pdf f(z). c. Are Z and W independent?
let x and y be random variables whose joint distributionus uniform over the half-disk: {(X,Y)|x^2+y^2 <=...
let x and y be random variables whose joint distributionus uniform over the half-disk: {(X,Y)|x^2+y^2 <= 1 and x>0}. what is the marginal density function of X for 0 <= x <=1? Answer is 4/pi * (1-x^2)^1/2. can anyone explain why the reciprocal of the area of semicircle is the density function of the f(X,Y)? Thanks
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT