   Chapter 9.3, Problem 32E ### 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
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# Special Probability Density Functions In Exercises 29-34, identify the probability density function. Then find the mean, variance, and standard deviation without integrating. f ( x ) = 5 3 e − 5 x / 3 ,      ( 0 , ∞ )

To determine

To calculate: The probability density function and then find the mean, variance and standard deviation.

Explanation

Given Information:

The probability distribution function is

f(x)=53e53.x,x(0,)

Formula used:

For exponential probability density function is f(x)=acax,0x<α,a>0 the expected value and mean can be found as:

u=1a

Variance formula is

v(x)=1a2

Standard deviation can be found by using formula: σ=v(x)

Calculation:

Consider the provided probability distribution function is

f(x)=53e53.x,x(0,)

Since, the formula for exponential probability density function is

f(x)=acax,0x<α,a>0

The expected value and mean can be found as:

u=1a

And variance formula is

v(x)=1a2

Standard deviation can be found by using formula: σ=v(x)

Now, compare the provided probability density function f(x)=53e53

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