Chapter 13.7, Problem 34E

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

Chapter
Section

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Find the mean of the probability distribution if the probability density function is f ( x ) = { 0 c / x 4   otherwise if  x   ≥  10

To determine

To calculate: The mean of the probability distribution if the probability density function is f(x)={cx4x100otherwise.

Explanation

Given Information:

The provided probability density function is, f(x)={cx4x100otherwise.

Formula used:

The mean of a probability distribution is,

μ=xf(x)dx

Where, x is a continuous random variable and f(x) is a probability density function.

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

af(x)dx=limbabf(x)dx

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,

xndx=xn+1n+1+C

Where, n1.

Calculation:

Consider the provided probability density function, f(x)={cx4x100otherwise.

Use the formula for mean of a probability distribution.

μ=xf(x)dx

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

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