   Chapter 13.7, Problem 30E ### Mathematical Applications for the ...

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

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

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

# For what value of c is the function f ( x ) = { c / x 2   if  x ≥ 100 0         otherwise a probability density function?

To determine

To calculate: The value of c in the function f(x)={cx3x1000otherwise so that this function is a probability density function.

Explanation

Given Information:

The provided function is,

f(x)={cx3x1000otherwise

Formula used:

If f(x)0 for all x, then for a continuous random variable x, f is a probability density function if and only if,

f(x)dx=1

If the limit defining the improper integral is a unique finite number, then integral converges else it diverges,

af(x)dx=limbabf(x)dx

According to the power rule of integrals,

xndx=xn+1n+1+C

Calculation:

Consider the provided function,

f(x)={cx3x1000otherwise

Now, if 1000dx+100cx3dx=1 then the function will be probability density function.

Use the formula,

af(x)dx=limbabf(x)dx

To rewrite the integral as,

f(x)dx=1000dx+100cx3dx</

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