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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 ( t ) = 1 9 e t / 9 , [ 0 , )

To determine

To calculate: The mean and median of the probability density functions f(t)=19et9.

Explanation

Given Information:

The probability distribution function is,

f(t)=19et9,[0,)

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(t)=19et9;x[0,)

Consider the primary equation to find mean of probability density function

μ=abtf(t)dt

Now substitute 19et9 for f(t) and interval [a,b][0,) is primary equation,

μ=0[19tet9]dt

Integrating primary equation,

μ=0[19tet9]dt=19[tet9dtdtdtet9dtdt]0=19[(9)tet9

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