Chapter 13.7, Problem 33E

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11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

Find the mean of the probability distribution if the probability density function is

To determine

**To calculate:** The mean of the probability distribution if the probability density function is

Explanation

**Given Information:**

The provided probability density function is,

**Formula used:**

The mean of a probability distribution is,

Where, *x* is a continuous random variable and

The improper integral in form of a limit of integral is,

Where *a* and *b* are the limit of the integral and for the integral to be converge, the both limit must be a finite number otherwise the integral diverges.

The simple power rule of integral,

Where,

**Calculation:**

Consider the provided probability density function,

Use the formula for mean of a probability distribution.

Break the limit of the provided integral at 10 and put the corresponding function

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