Explanation Formula used: If X is an exponential random variable, then the probability density function is f ( x ) = { ( 1 λ ) e − x λ if x ≥ 0 0 otherwise . The respective cumulative distribution function is F ( x ) = { 1 − e − x λ if x ≥ 0 0 otherwise . Calculation: Given that X is exponentially distributed with λ = 1 2 . Substitute λ = 1 2 in the above formula to obtain the probability density function. f ( x ) = { ( 1 ( 1 2 ) ) e − x ( 1 2 ) if x ≥ 0 0 otherwise = { 2 e − 2 x if x ≥ 0 </

Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.

15th Edition

ISBN: 9781323047620

Author: Barnett, Ziegler, Byleen

Publisher: Pearson Education

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Chapter 11.4, Problem 3E

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To find: The probability density function f and the associated cumulative distribution function F for the exponential distributed random variable X with λ=12.

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Chapter 11.4, Problem 2E

Chapter 11.4, Problem 4E

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Chapter 11 Solutions

Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.

Ch. 11.1 - Evaluate the following, if it converges: 3dx(x1)2.Ch. 11.1 - Prob. 2MP Ch. 11.1 - Prob. 3MP Ch. 11.1 - Prob. 4MP Ch. 11.1 - Prob. 5MP Ch. 11.1 - Prob. 6MP Ch. 11.1 - Prob. 1ED Ch. 11.1 - Prob. 2ED Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E

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The probability density function f and the associated cumulative distribution function F for the exponential distributed random variable X with λ = 1 2 .

Solution Summary: The author explains the probability density function f and cumulative distribution function F for the exponential distributed random variable X with lambda =12.

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To find: The probability density function f and the associated cumulative distribution function F for the exponential distributed random variable X with λ=12.

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Chapter 11 Solutions