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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
Publisher: Cengage Learning
ISBN: 9781305860919

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BuyFindarrow_forward

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
Publisher: Cengage Learning
ISBN: 9781305860919
Chapter 9, Problem 50RE
Textbook Problem
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Special Probability Density Functions In Exercises 49–54, identify the probability density function. Then find the mean, variance, and standard deviation without integrating.

f ( x ) = 1 9 , [ 0 , 9 ]

To determine

The probability density function of f(x)=19 over the interval [0,9] and calculate the mean, variance and standard deviation without integration.

Explanation of Solution

Given Information:

The probability density function:

f(x)=19 over the interval [0,9]

Consider the provided probability density function.

f(x)=19 over the interval [0,9]

The provided probability density function can be written as,

f(x)=190 for [0,9]

The uniform probability function is defined as,

f(x)=1ba,axb

This shows that the provided probability density function is an uniform probability density function with a=0,b=9.

The formula for mean and variance of uniform probability density function is defined as,

μ=a+b2

V(x)=(ba)212

The provided uniform probability density function shows that a=0,b=9. Substitute these values in the formulas for mean and variance to calculate the same

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Chapter 9 Solutions

Calculus: An Applied Approach (MindTap Course List)
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