Chapter 15.6, Problem 51E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

The joint density function for random variables *X*, *Y*, and *Z* is *f*(*x, y, z*) = *Cxyz* if 0 ≤ *x* ≤ 2, 0 ≤ *y* ≤ 2, 0 ≤ *z* ≤ 2, and *f* (*x, y, z*) = 0 otherwise.

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

(b) Find *P*(*X* ≤ l, *Y* ≤ 1,*Z* ≤ 1).

(c) Find *P* (*X* + *Y* + *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:**

(b)

To determine

**To find:** The value of

(c)

To determine

**To find:** The value of

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