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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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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 ( 1 , 2 x ) , [ 0 , 1 2 ]

To determine

To calculate: The mean and median of the probability density functions f(x)=4(12x).

Explanation

Given Information:

The probability distribution function is,

f(x)=4(12x), where interval is [0,12].

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)=4(12x);x[0,12]

Consider the primary equation to find mean,

μ=abxf(x)dx

Now substitute 4(12x) for f(x) and interval [a,b][0,12] in primary equation,

μ=012xf(x)dx=012x4(12x)dx=0124x8x2dx

Integrating primary equation:

μ=4[x2]01228[x3]0123=2[(12)20]83

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