   Chapter 9.2, Problem 17E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
1 views

# Making a Probability Density Function In Exercises 13–18, find the constant k such that the function f is a probability density function over the given interval. f ( x ) = k e − x / 2 ,       [ 0 , ∞ )

To determine

To calculate: The value of constant ‘k’ for which the function f(x)=kex2 is a probability density function over the interval [0,).

Explanation

Given Information:

The function f(x)=kex2 is a probability density function over the interval [0,).

Formula used:

Consider a function f of a continuous random variables x whose set of values is the interval [a,b] A function is a probability density function when it is non-negative and continuous on the interval [a,b] and when,

abf(x)dx=1

Calculation:

Consider the function,

f(x)=kex2

As the function is a probability density function over the interval [0,).

Therefore, f(x) is continuous and non-negative over the interval [0,).

Also 0f(x)dx=1 as,

0f(x)dx=10ke

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### 27r63s2t4

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### Find f in terms of f and g. h(x) = f(g(sin 4x))

Single Variable Calculus: Early Transcendentals

#### The harmonic series is: 1 + 2 + 3 + 4 + …

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 