Question

For continuous random variables X and Y with joint probability density function. f(x,y) = xe−(x+y) when...

For continuous random variables X and Y with joint probability density function. f(x,y) = xe−(x+y) when x > 0 and y > 0 f(x,y) = 0 otherwise

a. Find the conditional density F xly (xly)

b. Find the marginal probability density function fX (x)

c. Find the marginal probability density function fY (y).

d. Explain if X and Y are independent

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
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) = xe^−x(y+1), 0 , 0< x < ∞,0 < y < ∞ otherwise (a) Are X and Y independent or not? Why? (b) Find the conditional density function of Y given X = 1.(
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 X and Y be a random variables with the joint probability density function fX,Y (x,...
Let X and Y be a random variables with the joint probability density function fX,Y (x, y) = { cx2y, 0 < x2 < y < x for x > 0 0, otherwise }. compute the marginal probability density functions fX(x) and fY (y). Are the random variables X and Y independent?.
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...
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]
Let fX,Y be the joint density function of the random variables X and Y which is...
Let fX,Y be the joint density function of the random variables X and Y which is equal to fX,Y (x, y) = { x + y if 0 < x, y < 1, 0 otherwise. } Compute the probability density function of X + Y . Referring to the problem above, compute the marginal probability density functions fX(x) and fY (y). Are the random variables X and Y independent?
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 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?
The joint probability density function of two random variables (X and Y) is given by fX,Y...
The joint probability density function of two random variables (X and Y) is given by fX,Y (x, y) = ( C √y (y ^(α+1)) exp {( − y(2β+x ^2 ) )/2 } , x ∈ (−∞,∞), y ∈ [0,∞), 0 otherwise. (a) Find C. (b) Find the marginal density of Y . What type of distribution does Y follow? (c) Find the conditional density of X | Y . What type of distribution is this?
Suppose that the joint probability density function of the random variables X and Y is f(x,...
Suppose that the joint probability density function of the random variables X and Y is f(x, y) = 8 >< >: x + cy^2 0 ≤ x ≤ 1, 0 ≤ y ≤ 1 0 otherwise. (a) Sketch the region of non-zero probability density and show that c = 3/ 2 . (b) Find P(X + Y < 1), P(X + Y = 1) and P(X + Y > 1). (c) Compute the marginal density function of X and Y...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT