Explanation Given information: The density function of the exponential random variable is f ( x ) = 1.5 e − 1.5 x Explanation: 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 1.5 e − 1.5 x with f ( x ) = k e − k x This indicates k = 1.5 . Substitute k = 1.5 in E ( X ) = 1 k . ⇒ E ( X ) = 1 1

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Chapter 12.4, Problem 4E

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The expected value E(X) and variance Var(X) of the exponential random variable with the density function 1.5e−1.5x

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Chapter 12.4, Problem 3E

Chapter 12.4, Problem 5E

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The expected value E ( X ) and variance Var ( X ) of the exponential random variable with the density function 1.5 e − 1.5 x

Solution Summary: The author explains the density function of the exponential random variable f(x)=1.5e-1.5x.

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The expected value E(X) and variance Var(X) of the exponential random variable with the density function 1.5e−1.5x

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