   Chapter 13.7, Problem 27E ### 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

# Show that the function f ( x ) = { 200 x 3   if  x ≥ 10 0        otherwise is a probability density function.

To determine

To prove: The provided function f(x)={200x3if x100otherwise is a probability density function.

Explanation

Given Information:

The provided function is,

f(x)={200x3if x100otherwise

Formula used:

f Is a probability density function for a continuous random variable x, where f(x)0 for all x 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

Proof:

Consider the provided function,

f(x)={200x3if x100otherwise

Now, if 90dx+10200x3dx is 1 then the function will be probability density function

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