Chapter 15.4, Problem 29E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Suppose *X* and *Y* are random variables with joint density function

(a) Verify that *f* is indeed a joint density function.

(b) Find the following probabilities.

(i) *P*(*Y*

(ii) *P*(*X*
*Y*

(c) Find the expected values of *X* and *Y.*

(a)

To determine

**To verify:** The given function is the joint density function.

Explanation

**Property used:**

If the given function

**Formula used:**

If

**Given:**

The joint density function,

**Calculation:**

Obtain

Find the value of the double integral using the equation (1),

(b) (i)

To determine

**To find:** The value of

(ii)

To determine

**To find:** The value of

(c)

To determine

**To find:** The expected value of *X* and *Y*.

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