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10th Edition

Ron Larson

Publisher: Cengage Learning

ISBN: 9781305860919

Chapter 9, Problem 22RE

Textbook Problem

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**Verifying a Probability Density Function** In Exercises 21–24, show that the function is a probability density function over the given interval.

To determine

**To prove:** The function

**Given Information:**

The function

**Formula used:**

A function *f* of a continuous random variable *x* in the interval

The integration formula:

The Fundamental theorem:

**Proof:**

Consider the provided function

Consider any value

So,

So, the function *f* is continuous and nonnegative for all values on the interval

Now, show that

Evaluate the integral

Use distributive property

Calculus: An Applied Approach (MindTap Course List)

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