Let f(x, y) = (3/16)xy2, 0 x 2, 0 y 2, be the joint pdf of X and Y. (a) Find fX (x) and

Chapter 4, Problem 4.4-1

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QUESTION:

Let f(x, y) = (3/16)xy2, 0 x 2, 0 y 2, be the joint pdf of X and Y. (a) Find fX (x) and fY (y), the marginal probability density functions. (b) Are the two random variables independent? Why or why not? (c) Compute the means and variances of X and Y. (d) Find P(X Y).

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QUESTION:

Let f(x, y) = (3/16)xy2, 0 x 2, 0 y 2, be the joint pdf of X and Y. (a) Find fX (x) and fY (y), the marginal probability density functions. (b) Are the two random variables independent? Why or why not? (c) Compute the means and variances of X and Y. (d) Find P(X Y).

ANSWER:

Problem 4.4.1

Let , be the joint pdf of X and Y.

(a) Find  and , the marginal probability density function.

(b) Are the two random variables independent? Why or why not?

(c) Compute the means and variances of X and Y.

(d) Find P(X  Y).

                                                               Step by Step Solution

Step 1 of 6

Given that joint pdf of the  and  as,

 

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