To determine To find: The expected value, variance and standard deviation. Explanation Given: The function f ( x ) = 8 3 x 3 is a probability density function on the interval [ 1 , 2 ] . Definition used: “If X is a continuous random variable with probability function f on [ a , b ] , then the expected value of X is E ( X ) = μ = ∫ a b x f ( x ) d x The variance of X is V a r ( X ) = ∫ a b ( x − μ ) 2 f ( x ) d x , and the standard deviation of X is σ = V a r ( X ) ”. Calculation: Consider the given function f ( x ) = 8 3 x 3 on the interval [ 1 , 2 ] . Use the above mentioned definition and find expectation. E ( X ) = μ = ∫ 1 2 x f ( x ) d x = ∫ 1 2 x × 8 3 x 3 d x = 8 3 ∫ 1 2 x − 2 d x On further simplification the above expression becomes, E ( X ) = 8 3 [ − 1 x ] 1 2 = − 8 3 [ 1 2 − 1 ] = − 8 3 ( − 1 2 ) = 4 3 Thus, the expected value is E ( X ) = 4 3 . Use the above mentioned definition and find variance

Calculus With Applications, Books a la Carte Plus MyLab Math Package (11th Edition)

11th Edition

ISBN: 9780133886849

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 11.2, Problem 1YT

To determine

To find: The expected value, variance and standard deviation.

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Calculus With Applications, Books a la Carte Plus MyLab Math Package (11th Edition)

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