   Chapter 9.3, Problem 26E ### 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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# Finding the Mean and Median In Exercises 23-28, find the mean and median of the probability density function. See Example 4. f ( x ) = 4 3 − 2 3 x , [ 0 , 1 ]

To determine

To calculate: The mean and median of the probability density functions f(x)=4323x.

Explanation

Given Information:

The probability distribution function is,

f(x)=4323x where interval is [0,1].

Formula used:

The formula to find the mean of probability distribution function is:

μ=abxf(x)dx

where, μ is mean or expected value of probability distribution function f(x), [a,b] is given interval.

The formula to find the median, for probability distribution function f(x) is median of x is number m such that amf(x)dx=0.5.

Calculation:

Consider the given equation,

f(x)=4323x;x[0,1]

Consider the primary equation to find mean

μ=abxf(x)dx

Now substitute 4323x for f(x) and interval [a,b][0,1] is primary equation.

μ=01x[4323x]dx=43[x2]01223[x2]013=2329=2329

Solve further,

μ=01x[4323x]dx=49

Substitute 4323x for f(x) and a=0,b=1 in the given formula

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