   Chapter 9.3, Problem 13E ### 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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# Using Two Methods In Exercises 13-16, find the variance of the probability density function using two methods. f ( x ) = 2 9 x ,   [ 0 ,   3 ]

To determine

To calculate: The variance of probability density function f(x)=29x.

Explanation

Given Information:

The probability density function is;

f(x)=29x

And interval is [0,3].

Formula used:

The formula for mean or expectation is;

μ=E(x)=abxf(x)dx

The variance is given by;

V(x)=ab(xμ)2f(x)dx

The integration of f(x)=xn is;

xndx=xn+1n+1+c,n1

Calculation:

Consider the given function

f(x)=29x

So, mean can be calculated as;

μ=E(x)=abxf(x)dx=03x29xdx=2903x2dx

Further calculation shows that;

μ=2903x2dx=29[x33]03=29=2

Now variance can be calculated by use of formula V(x

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