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10th Edition

Ron Larson

Publisher: Cengage Learning

ISBN: 9781305860919

Chapter 9, Problem 48RE

Textbook Problem

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**Finding the Mean and Median** In Exercises 45–48, find the mean and median of the probability density function.

**Special Probability Density Functions** In Exercises 49–54, identify the probability density function. Then find the mean, variance, and standard deviation without integrating.

To determine

**To calculate:** The mean and median of probability density function

**Given Information:**

The probability density function is defined as

**Formula used:**

Mean:

If *f* is the probability density function *f* for a continuous random variable *x* for the interval *a* and *b* are real numbers, then the mean of *x* is defined by the formula,

Median:

If *f* is the probability density function *f* for a continuous random variable *x* for the interval *a* and *b* are real numbers, then the median of *x* is defined by the formula,

**Calculation:**

Consider the provided probability density function is,

Use the formula

So,

Use the formula

Integrate to calculate *v* as,

So, the mean is calculated as,

Calculus: An Applied Approach (MindTap Course List)

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