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10th Edition

Ron Larson

Publisher: Cengage Learning

ISBN: 9781305860919

Chapter 9, Problem 13TYS

Textbook Problem

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In Exercises 13–15, use the given probability density function over the indicated interval to find the expected value, variance, and standard deviation of the random variable.

To determine

**To calculate:** The expected value, variance and standard deviation of probability density function

**Given Information:**

The probability density function is defined as

**Formula used:**

For any probability density function *f* of a continuous random variable *x* over the interval *x* is defined as,

For any probability density function *f* of a continuous random variable *x* over the interval *x* is defined as,

Here *x*.

For any probability density function *f* of a continuous random variable *x* over the interval *x* is defined as,

**Calculation:**

Consider the provided probability density function.

Use the formula

So,

Use the formula

Use the Fundamental theorem

Thus, the expected value of the provided probability density function is

Now calculate the variance.

The mean of the probability density function is obtained as

Now use the formula

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