Explanation Given: The function f ( x ) = 1 11 ( 1 + 3 x ) is a probability density function on the interval [ 4 , 9 ] . 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 ) = 1 11 ( 1 + 3 x ) on the interval [ 4 , 9 ] . Use the above mentioned definition and find expectation. E ( X ) = μ = ∫ 4 9 x f ( x ) d x = 1 11 ∫ 4 9 x ( 1 + 3 x ) d x = 1 11 ∫ 4 9 ( x + 3 x 1 2 ) d x On further simplification the above expression becomes, E ( X ) = 1 11 [ x 2 2 + 3 x 1 2 + 1 1 2 + 1 ] 4 9 = 1 11 [ ( 9 2 2 + 3 × 2 3 × 9 3 2 ) − ( 4 2 2 + 3 × 2 3 × 4 3 2 ) ] = 1 11 [ 81 2 + 54 − 8 − 16 ] = 141 22 ≈ 6

Calculus with Applications (11th Edition)

11th Edition

ISBN: 9780321979421

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

Publisher: PEARSON

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Chapter 11.2, Problem 6E

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To find: The expected value, variance and standard deviation for the function f(x)=111(1+3x) .

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Chapter 11.2, Problem 5E

Chapter 11.2, Problem 7E

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Chapter 11 Solutions

Calculus with Applications (11th Edition)

Ch. 11.1 - YOUR TURN 1 Repeat Example 1(a) for the function...Ch. 11.1 - Prob. 2YT Ch. 11.1 - Prob. 3YT Ch. 11.1 - Prob. 4YT Ch. 11.1 - Prob. 1WE Ch. 11.1 - Prob. 2WE Ch. 11.1 - Prob. 3WE Ch. 11.1 - Decide whether the functions defined as follows...Ch. 11.1 - Decide whether the functions defined as follows...Ch. 11.1 - Decide whether the functions defined as follows...

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The expected value, variance and standard deviation for the function f ( x ) = 1 11 ( 1 + 3 x ) .

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To find: The expected value, variance and standard deviation for the function f(x)=111(1+3x) .

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Chapter 11 Solutions