Question

2. 2. The joint probability density function of X and Y is given by                               &n

2.

2. The joint probability density function of X and Y is given by                                          

       f(x,y) = (6/7)(x² + xy/2), 0 < x < 1, 0 < y < 2.     f(x,y) =0 otherwise

a) Compute the marginal densities of X and Y. b) Are X and Y independent. c) Compute the   conditional density function f(y|x) and check restrictions on function you derived d) probability P{X+Y<1} [5+5+5+5 = 20]

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
2. The joint probability density function of X and Y is given by                               &nbsp
2. The joint probability density function of X and Y is given by                                                  f(x,y) = (6/7)(x² + xy/2), 0 < x < 1, 0 < y < 2.     f(x,y) =0 otherwise a) Compute the marginal densities of X and Y. b) Are X and Y independent. c) Compute the   conditional density function f(y|x) and check restrictions on function you derived d) probability P{X+Y<1}
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...
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
The joint probability density function of two random variables X and Y is f(x, y) =...
The joint probability density function of two random variables X and Y is f(x, y) = 4xy for 0 < x < 1, 0 < y < 1, and f(x, y) = 0 elsewhere. (i) Find the marginal densities of X and Y . (ii) Find the conditional density of X given Y = y. (iii) Are X and Y independent random variables? (iv) Find E[X], V (X) and covariance between X and Y .
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
A joint density function is given by fX,Y (x, y) = ( kx, 0 < x...
A joint density function is given by fX,Y (x, y) = ( kx, 0 < x < 1, 0 < y < 1 0, otherwise. (a) Calculate k (b) Calculate marginal density function fX(x) (c) Calculate marginal density function fY (y) (d) Compute P(X < 0.5, Y < 0.1) (e) Compute P(X < Y ) (f) Compute P(X < Y |X < 0.5) (g) Are X and Y independent random variables? Show your reasoning (no credit for yes/no answer). (h)...
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.(
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...
Let X and Y have joint density f(x, y) = 6/7(x + y)^2 if 0 ≤...
Let X and Y have joint density f(x, y) = 6/7(x + y)^2 if 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, 0 otherwise, where c is a positive constant. Compute the marginal densities of X and of Y (be explicit about all cases!). Compute P(Y + 2X < 1). Determine whether X and Y are independent. Justify your answer.
Given the joint probability density function f ( x , y ) for 0 < x...
Given the joint probability density function f ( x , y ) for 0 < x < 3 and 0 < y < 2 x^2y/81 Find the conditional probability distribution of X=1 given that Y = 1 f ( x , y ) = x^2 y/ 81 . F i n d the conditional probability distribution of X=1 given that Y = 1. i . e . f (X ∣ y = 1 )( 1 )
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT