Chapter 15.6, Problem 52E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Suppose *X, Y,* and *Z* are random variables with joint density function
*f* (*x, y, z*) = 0 otherwise.

(a) Find the value of the constant *C*.

(b) Find *P(X* ≤ 1, *Y* ≤ 1).

(c) Find *P(X* ≤ 1, *Y* ≤ 1, Z ≤ 1).

(a)

To determine

**To find:** The value of a constant *C*.

Explanation

**Property used:**

If the given function

**Formula used:**

If

**Given:**

The joint density function,

**Calculation:**

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

(b)

To determine

**To find:** The value of

(c)

To determine

**To find:** The value of

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