Question

Suppose X and Y are jointly continuous random variables with probability density function

Suppose X and Y are jointly continuous random variables with probability density function f(х+ у)={1/6(x + y), 0 < х < 1, 0 < у < 3; 0 , else} 

a) Find E[XY]. 

b) Are X and Y independent? Justify your answer citing an appropriate theorem.

3 0
Add a comment Improve this question Transcribed image text
Know the answer?
Add Answer to:
Suppose X and Y are jointly continuous random variables with probability density function
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. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions
  • f(x,y)=0 2. (20 marks) Suppose X and Y are jointly continuous random variables with probability density...

    f(x,y)=0 2. (20 marks) Suppose X and Y are jointly continuous random variables with probability density function fc, 0<x<1, 0<y<1, x + y>1 else a) (2.5 marks) Find the constant, c, so that this is valid joint density function. b) (5 marks) Find P(Y > 2X). c) (5 marks) Find P(X>0.5 Y = 0.75). d) (5 marks) Find P(X>0.5 Y <0.75). e) (2.5 marks) Are X and Y independent? Justify your answer citing an appropriate theorem.

  • Suppose that X and Y are jointly continuous random variables with joint probability density function f(x,y)...

    Suppose that X and Y are jointly continuous random variables with joint probability density function f(x,y) = {12rºy, 1 0, 0<x<a, 0<y<1 otherwise i) Determine the constant a ii) Find P(0<x<0.5, O Y<0.25) HE) Find the marginal PDFs fex) and y) iv) Find the expected value of X and Y. Le. E(X) and E(Y) v) Are X and Y independent? Justify your answer.

  • f(x,y)= 0 1. (15 marks) Suppose X and Y are jointly continuous random variables with probability...

    f(x,y)= 0 1. (15 marks) Suppose X and Y are jointly continuous random variables with probability density function 12, 0<x<1, 0<y<0.5 else a) (5 marks) Find P(X - Y <0.25). b) (5 marks) Find P(XY <0.30). c) (5 marks) Find V (2x - 5Y+30).

  • Let X and Y be jointly continuous random variables with joint probability density given by f(x,...

    Let X and Y be jointly continuous random variables with joint probability density given by f(x, y) = 12/5(2x − x2 − xy) for 0 < x < 1, 0 < y < 1 0 otherwise (a) Find the marginal densities for X and Y . (b) Find the conditional density for X given Y = y and the conditional density for Y given X = x. (c) Compute the probability P(1/2 < X < 1|Y =1/4). (d) Determine whether...

  • Let X and Y be jointly continuous random variables with joint probability density given by f(x,...

    Let X and Y be jointly continuous random variables with joint probability density given by f(x, y) = 12/5(2x − x2 − xy) for 0 < x < 1, 0 < y < 1 0 otherwise (a) Find the marginal densities for X and Y . (b) Find the conditional density for X given Y = y and the conditional density for Y given X = x. (c) Compute the probability P(1/2 < X < 1|Y =1/4). (d) Determine whether...

  • 55. Let X and Y be jointly continuous random variables with joint density function fx.y(x,y) be-3y...

    55. Let X and Y be jointly continuous random variables with joint density function fx.y(x,y) be-3y -a < x < 2a, 0) < y < 00, otherwise. Assume that E[XY] = 1/6. (a) Find a and b such that fx,y is a valid joint pdf. You may want to use the fact that du = 1. u 6. и е (b) Find the conditional pdf of X given Y = y where 0 <y < . (c) Find Cov(X,Y). (d)...

  • Suppose that X and Y are jointly continuous random variables with joint density f(x, y) =...

    Suppose that X and Y are jointly continuous random variables with joint density f(x, y) = ( ye−xy 0 < x < ∞, 1 < y < 2 0 otherwise (a) Given that X > 1, what is the expected value of Y ? That is, calculate E[Y | X > 1]. (b) Given that X > Y , what is the expected value of X? For this part, you are only required to set up the requisite integrals, but...

  • The continuous random variables, X and Y , have the following joint probability density function:   ...

    The continuous random variables, X and Y , have the following joint probability density function:    f(x,y) = 1/6(y2 + x3), −1 ≤ x ≤ 1, −2 ≤ y ≤ 1, and zero otherwise. (a) Find the marginal distributions of X and Y. (b) Find the marginal means and variances. (c) Find the correlation of X and Y. (d) Are the two variables independent? Justify.

  • The joint probability density function for continuous random variables X and Y is given below. f...

    The joint probability density function for continuous random variables X and Y is given below. f (x) =   x + y, 0 < x < 1, 0 < y < 1 if;                                                                          0,         degilse. (a) Show that this is a joint density function. (b) Find the marginal density of X . (c) Find the marginal density of Y . (d) Given Y = y find the conditional density of X . (e) P ( 1/2 < X < 1|Y =...

  • The joint probability density function for continuous random variables X and Y is given below. f...

    The joint probability density function for continuous random variables X and Y is given below. f (x) =   x + y, 0 < x < 1, 0 < y < 1 if;                                                                          0,         degilse. (a) Show that this is a joint density function. (b) Find the marginal density of X . (c) Find the marginal density of Y . (d) Given Y = y find the conditional density of X . (e) P ( 1/2 < X < 1|Y =...

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT