Explanation Given: The function f ( x ) = x 8 − 1 4 is a probability density function on the interval [ 2 , 6 ] . 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 2 f ( x ) d x − ( μ ) 2 . And the standard deviation of X is σ ≈ V a r ( X ) ”. Calculation: Consider the given function f ( x ) = x 8 − 1 4 on the interval [ 2 , 6 ] . Use the above mentioned definition and find expectation. E ( X ) = μ = ∫ 2 6 x f ( x ) d x = ∫ 2 6 x ( x 8 − 1 4 ) d x = ∫ 2 6 ( x 2 8 − x 4 ) d x On further simplification the above expression becomes, E ( X ) = [ x 3 24 − x 2 8 ] 2 6 = 1 24 [ 6 3 − 2 3 ] − 1 8 [ 6 2 − 2 2 ] = 1 24 [ 216 − 8 ] − 1 8 [ 36 − 4 ] = 1 24 × 208 − 1 8 × 32 On further simplification the above expression becomes, E ( X ) = 26 3 − 4 = 14 3 ≈ 4

Finite Mathematics and Calculus with Applications (10th Edition)

10th Edition

ISBN: 9780321979407

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

Publisher: PEARSON

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Chapter 18.2, Problem 3E

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To find: The expected value, variance and standard deviation for the function f(x)=x8−14 .

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Chapter 18.2, Problem 2E

Chapter 18.2, Problem 4E

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Chapter 18 Solutions

Finite Mathematics and Calculus with Applications (10th Edition)

Ch. 18.1 - Prob. 1YT Ch. 18.1 - Prob. 2YT Ch. 18.1 - Using the probability density function of Example...Ch. 18.1 - Use part (a) of Example 5 to calculate the...Ch. 18.1 - Evaluate each of the following integrals. (Sec....Ch. 18.1 - Prob. 2WE Ch. 18.1 - Prob. 3WE Ch. 18.1 - Decide whether the functions defined as follows...Ch. 18.1 - Prob. 2E Ch. 18.1 - Prob. 3E

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Pulliam found that the time (in...Ch. 18.3 - Life Expectancy According to the National Center...Ch. 18.3 - Prob. 45E Ch. 18.3 - Prob. 46E Ch. 18.3 - Prob. 47E Ch. 18.3 - Prob. 48E Ch. 18.3 - Prob. 49E Ch. 18.3 - Prob. 50E Ch. 18.3 - Prob. 51E Ch. 18.3 - Prob. 52E Ch. 18.3 - Prob. 53E Ch. 18.3 - Prob. 54E Ch. 18 - Prob. 1RE Ch. 18 - Prob. 2RE Ch. 18 - Prob. 3RE Ch. 18 - Prob. 4RE Ch. 18 - Prob. 5RE Ch. 18 - Prob. 6RE Ch. 18 - Prob. 7RE Ch. 18 - Prob. 8RE Ch. 18 - Prob. 9RE Ch. 18 - Prob. 10RE Ch. 18 - Prob. 11RE Ch. 18 - Prob. 12RE Ch. 18 - Prob. 13RE Ch. 18 - Prob. 14RE Ch. 18 - Prob. 15RE Ch. 18 - Prob. 16RE Ch. 18 - Prob. 17RE Ch. 18 - Prob. 18RE Ch. 18 - Prob. 19RE Ch. 18 - Prob. 20RE Ch. 18 - Prob. 21RE Ch. 18 - Prob. 22RE Ch. 18 - Prob. 23RE Ch. 18 - Prob. 24RE Ch. 18 - Prob. 25RE Ch. 18 - Prob. 26RE Ch. 18 - Prob. 27RE Ch. 18 - Prob. 28RE Ch. 18 - Prob. 29RE Ch. 18 - Prob. 30RE Ch. 18 - Prob. 31RE Ch. 18 - Prob. 32RE Ch. 18 - Prob. 33RE Ch. 18 - Prob. 34RE Ch. 18 - Prob. 35RE Ch. 18 - Prob. 36RE Ch. 18 - Prob. 37RE Ch. 18 - Prob. 38RE Ch. 18 - Prob. 39RE Ch. 18 - Prob. 40RE Ch. 18 - Prob. 41RE Ch. 18 - Prob. 42RE Ch. 18 - Prob. 43RE Ch. 18 - Prob. 44RE Ch. 18 - Prob. 45RE Ch. 18 - Prob. 46RE Ch. 18 - Prob. 47RE Ch. 18 - Prob. 48RE Ch. 18 - Prob. 49RE Ch. 18 - Prob. 50RE Ch. 18 - Prob. 51RE Ch. 18 - Prob. 52RE Ch. 18 - Prob. 53RE Ch. 18 - Prob. 54RE Ch. 18 - Prob. 55RE Ch. 18 - Prob. 56RE Ch. 18 - Prob. 57RE Ch. 18 - Prob. 58RE Ch. 18 - Prob. 59RE Ch. 18 - Prob. 60RE Ch. 18 - Prob. 61RE Ch. 18 - Prob. 62RE

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The expected value, variance and standard deviation for the function f ( x ) = x 8 − 1 4 .

Solution Summary: The author calculates the expected value, variance, and standard deviation for the function f(x)=x

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To find: The expected value, variance and standard deviation for the function f(x)=x8−14 .

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Chapter 18 Solutions