Explanation Given information: The density function of the exponential random variable is f ( x ) = 0.2 e − 0.2 x . Explanation: Let X be a random variable with an exponential density function f ( x ) = k e − k x ; x ≥ 0 , for some k > 0 . Then, E ( X ) = 1 k and Var ( X ) = 1 k 2 . Compare the given exponential density function 0.2 e − 0.2 x with f ( x ) = k e − k x This indicates, k = 0.2 Substitute k = 0

Student Solutions Manual for Calculus & Its Applications and Calculus & Its Applications, Brief Version

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Author: Larry J. Goldstein, David I Lay, David I. Schneider, Nakhle H. Asmar

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Chapter 12.4, Problem 3E

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The expected value E(X) and variance Var(X) of the exponential random variable with the density function 0.2e−0.2x

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Chapter 12.4, Problem 2E

Chapter 12.4, Problem 4E

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Chapter 12 Solutions

Student Solutions Manual for Calculus & Its Applications and Calculus & Its Applications, Brief Version

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The expected value E ( X ) and variance Var ( X ) of the exponential random variable with the density function 0.2 e − 0.2 x

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The expected value E(X) and variance Var(X) of the exponential random variable with the density function 0.2e−0.2x

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Chapter 12 Solutions