   Chapter 13.7, Problem 32E ### 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

# Find the value of c (in terms of k) so that f ( x ) = { c e − k x      if  x ≥ 0 0            if  x <   0 is a probability density function.

To determine

To calculate: The value of c so that f(x)={cekx  x00       x<0 is a probability density function.

Explanation

Given Information:

The function is;

f(x)={cekx  x00       x<0

Formula used:

The integration of function f(x)=eax is given by;

eaxdx=eaxa+c

Here c is any arbitrary constant.

Calculation:

Consider the function,

f(x)={cekx  x00       x<0

The given function is a probability density function, which implies that,

f(x)dx=1

Integrate the function as;

f(x)dx=00dx+0ce

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