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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Verifying a Probability Density Function In Exercises 1-6, show that the function is a probability density function over the given interval. See Examples 1 and 2.

f ( x ) = 0.2 e 0.2 x ,  [0, )

To determine

To prove: The function, f(x)=5e5x is a probability density function over the interval [0,).

Explanation

Given Information:

The function, f(x)=5e5x over the interval [0,)

Proof:

Consider the function,

f(x)=5e5x

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

abf(x)dx=1

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

Now, evaluate abf(x)dx as,

0f(x)dx=05e5xdx=50e<

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