   Chapter 9.2, Problem 2CP ### 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

# Show that f ( x ) = 2 e − 2 x is a probability density function over the interval [0, ∞).

To determine

To prove: The given function f(x)=2e2x is a probability density function over the range [0,]

Explanation

Given Information:

The given function is f(x)=2e2x and range is [0,].

Formula Used:

If the f(x) is function over the interval [a,b]. Than the density function satisfies the given condition as,

abf(x)=1

Proof:

Consider the given function,

Now, apply the formula,

02e2xdx=2[e2x]02=[ee0]=e0<

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