   Chapter 9.3, Problem 28E ### 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 ( t ) = 2 5 e − 2 t / 5 , [ 0 , ∞ )

To determine

To calculate: The mean and median of the probability density functions f(t)=25e2t5.

Explanation

Given Information:

The probability distribution function is,

f(t)=25e2t5,[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)=25e2t5;x[0,)

Consider the primary equation to find mean of probability density function

μ=abtf(t)dt

Now substitute 25e2t5 for f(t) and interval [a,b][0,) is primary equation

μ=0te2t5dt

Integrating from 0 to ,

μ=25[[t.(te2t5)]00{dtdt0e2t5}dt]=[(52)[te2t5]0(52)0e2t5dt]25=[(52)[te2t5]0(52)(52)

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