Chapter 15.4, Problem 27E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

The joint density function for random variables *X* and *Y* is

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

(b) Find *P*(*X* ≤ 1, *Y* ≤ 1).

(c) Find *P*(*X* + *Y* ≤ 1).

(a)

To determine

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

Explanation

**Given:**

The joint density function,

The region *D* is

**Property used:**

The double integral value of the given function over *D* is always 1 that is

**Formula used:**

If

**Calculation:**

By the property mentioned above, the value of

From the given condition, the value of

(b)

To determine

**To find:** The value of

(c)

To determine

**To find:** The value of

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