Explanation Given: The function f ( x ) = 2 ( 1 − x ) is a probability density function on the interval [ 0 , 1 ] . 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 ) = 2 ( 1 − x ) on the interval [ 0 , 1 ] . Use the above mentioned definition and find expectation. E ( X ) = μ = ∫ 0 1 x f ( x ) d x = ∫ 0 1 2 x ( 1 − x ) d x = 2 ∫ 0 1 ( x − x 2 ) d x On further simplification the above expression becomes, E ( X ) = 2 [ x 2 2 − x 3 3 ] 0 1 = 2 [ 1 2 2 − 1 3 3

Finite Mathematics and Calculus with Applications

1st Edition

ISBN: 9781323188361

Author: Margaret Lial

Publisher: Pearson Education

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Chapter 18.2, Problem 4E

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To find: The expected value, variance and standard deviation for the function f(x)=2(1−x) .

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Chapter 18.2, Problem 3E

Chapter 18.2, Problem 5E

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Chapter 18 Solutions

Finite Mathematics and Calculus with Applications

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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The expected value, variance and standard deviation for the function f ( x ) = 2 ( 1 − x ) .

Solution Summary: The author calculates the expected value, variance, and standard deviation for the function f(x)=2 x.

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To find: The expected value, variance and standard deviation for the function f(x)=2(1−x) .

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Chapter 18 Solutions