Question

Let X 1 and X 2 have the joint probability distribution function ??(??1, ??2) = �...

Let X 1 and X 2 have the joint probability distribution function ??(??1, ??2) = � ??−(??1+??2) ??1 > 0, ??2 > 0 0 elsewhere Find ??(??1 + ??2) and ??(??1 + ??2).

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

Homework Answers

Answer #1

The marginal pdf of X2 is

The marginal pdf of X1 is

Since

So X1 and X2 are independent.

-------------------------------------------------------

The marginal pdfs of X1 and X2 are exponential distribution with parameter 1. So,

Since X1 and X2 are independent so

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
STAT 190 Let X and Y have the joint probability density function (PDF), f X,Y (x,...
STAT 190 Let X and Y have the joint probability density function (PDF), f X,Y (x, y) = kx, 0 < x < 1, 0 < y < 1 - x^2, = 0, elsewhere, where k is a constant. 1) What is the value of k. 2)What is the marginal PDF of X. 3) What is the E(X^2 Y).
Let X and Y have the joint probability density function f(x, y) = ⎧⎪⎪ ⎨ ⎪⎪⎩...
Let X and Y have the joint probability density function f(x, y) = ⎧⎪⎪ ⎨ ⎪⎪⎩ ke−y , if 0 ≤ x ≤ y < ∞, 0, otherwise. (a) (6pts) Find k so that f(x, y) is a valid joint p.d.f. (b) (6pts) Find the marginal p.d.f. fX(x) and fY (y). Are X and Y independent?
Let X be a random variable with probability density function given by f(x) = 2(1 −...
Let X be a random variable with probability density function given by f(x) = 2(1 − x), 0 ≤ x ≤ 1,   0, elsewhere. (a) Find the density function of Y = 1 − 2X, and find E[Y ] and Var[Y ] by using the derived density function. (b) Find E[Y ] and Var[Y ] by the properties of the expectation and the varianc
Let X and Y be two continuous random variables with joint probability density function ?(?, ?)...
Let X and Y be two continuous random variables with joint probability density function ?(?, ?) = { ? 2 + ?? 3 0 ≤ ? ≤ 1, 0 ≤ ? ≤ 2 0 ??ℎ?????? Find ?(? + ? ≥ 1). Sketch the surface in the ? − ? plane.
Let X and Y be two random variables having the joint probability density fxy= 24xy for...
Let X and Y be two random variables having the joint probability density fxy= 24xy for 0<x<1, 0<y<1, 0<x+y<1, o elsewhere. Find the joint probability density of Z = X + Y, and W = 2Y
Let X have the distribution that has the following probability density function: f(x)={2x,0<x<1        {0, Otherwise...
Let X have the distribution that has the following probability density function: f(x)={2x,0<x<1        {0, Otherwise Find the probability that X>0.5. Why is the probability 0.75 and not 0.5?
The joint probability distribution of X and Y is given by f(x) = { c(x +...
The joint probability distribution of X and Y is given by f(x) = { c(x + y) x = 0, 1, 2, 3; y = 0, 1, 2. 0 otherwise (1) Find the value of c that makes f(x, y) a valid joint probability density function. (2) Find P(X > 2; Y < 1). (3) Find P(X + Y = 4).
a) The joint probability density function of the random variables X, Y is given as f(x,y)...
a) The joint probability density function of the random variables X, Y is given as f(x,y) = 8xy    if  0≤y≤x≤1 , and 0 elsewhere. Find the marginal probability density functions. b) Find the expected values EX and EY for the density function above c) find Cov  X,Y .
1. Let (X; Y ) be a continuous random vector with joint probability density function fX;Y...
1. Let (X; Y ) be a continuous random vector with joint probability density function fX;Y (x, y) = k(x + y^2) if 0 < x < 1 and 0 < y < 1 0 otherwise. Find the following: I: The expectation of XY , E(XY ). J: The covariance of X and Y , Cov(X; Y ).
X and Y are continuous random variables. Their joint probability distribution function is : f(x,y) =...
X and Y are continuous random variables. Their joint probability distribution function is : f(x,y) = 1/5(y+2) , 0 < y < 1, y-1 < x < y +1 = 0, otherwise a) Find marginal density of Y, fy(y) b) Calculate E[X | Y = 0]
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT