Let R be the bounded region between y = x and y = x2. A

Chapter , Problem 13

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QUESTION:

Let R be the bounded region between y = x and y = x2. A random point (X, Y ) is selected from R. (a) Find the joint probability density function of X and Y . (b) Calculate the marginal probability density functions of X and Y . (c) Find E(X) and E(Y ).

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QUESTION:

Let R be the bounded region between y = x and y = x2. A random point (X, Y ) is selected from R. (a) Find the joint probability density function of X and Y . (b) Calculate the marginal probability density functions of X and Y . (c) Find E(X) and E(Y ).

ANSWER:

Step 1 of 6

Denoting by R the region bounded by the line  and , we have the joint density to be  to b some constant when  and  otherwise. Since the density must add to , we must have the constant to be the reciprocal of the area of.

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