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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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Special Probability Density Functions In Exercises 29-34, identify the probability density function. Then find the mean, variance, and standard deviation without integrating.

f ( x ) = 1 6 2 π e ( x 30 ) 2 / 72 , ( , )

To determine

To calculate: The mean, variance and standard deviation of the probability distribution f(x)=1σ2πe(x30)272 with <x< without performing integration.

Explanation

Given information:

The probability distribution is f(x)=1σ2πe(x30)272 with <x<.

Formula used:

The normal probability distribution function in the standard form:

f(x)=1σ2πe(xμ)22σ2,<x<

where,

μ is the expected value of the above function, σ is the standard deviation, and the variance is given by V=σ2

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