Explanation Given information: f ( x ) = 1 2 x , 1 ≤ x ≤ 4 . Formula used: Let X be a continuous random variable, whose possible values lie between A and B , and f ( x ) be the probability density function for X . Then, the expected value (average) of X is the number E ( X ) defined by, E ( X ) = ∫ A B x f ( x ) d x . And the variance of X is defined by, Var ( X ) = ∫ A B x 2 f ( x ) d x − ( E ( X ) ) 2 . Calculation: Let X be the continuous random variable with values between A = 1 and B = 4 with density function, f ( x ) = 1 2 x By using the formula of expected value, E ( X ) = ∫ 1 4 x f ( x ) d x = ∫ 1 4 x 1 2 x d x . = 1 2 ∫ 1 4 x x − 1 / 2 d x = 1 2 ∫ 1 4 x 1 / 2 d x = 1 2 ( 2 3 x 3 / 2 ) | 1 4

12th Edition

ISBN: 9780137590810

Author: Larry J. Goldstein, David C. Lay, David I. Schneider, Nakhle H. Asmar, William Edward Tavernetti

Publisher: PEARSON

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Chapter 12.3, Problem 1CYU

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To calculate: The expected value and variance of the random variable X whose density function is f(x)=12x, 1≤x≤4.

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Chapter 12.2, Problem 38E

Chapter 12.3, Problem 2CYU

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The expected value and variance of the random variable X whose density function is f ( x ) = 1 2 x , 1 ≤ x ≤ 4 .

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To calculate: The expected value and variance of the random variable X whose density function is f(x)=12x, 1≤x≤4.

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Chapter 12 Solutions