Explanation Definition used: If f ( x ) is the probability density function for continuous random variable X , then The Mean is, μ = E ( X ) = ∫ − ∞ ∞ x f ( x ) d x . The variance is, V ( X ) = ∫ − ∞ ∞ ( x − μ ) 2 f ( x ) d x . The standard deviation is, σ = V ( X ) . Calculation: The given function is f ( x ) = { 18 x if 0 ≤ x ≤ 1 3 0 otherwise . Compute the mean of the function by using above definition. μ = ∫ − ∞ ∞ x f ( x ) d x = 18 ∫ 0 1 3 x 2 d x = 6 [ x 3 ] 0 1 3 On further simplification, μ = 6 ( ( 1 3 ) 3 − 0 ) = 6 ( 1 27 ) = 2 9 Thus, the mean is 2 9

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Chapter 11.3, Problem 4E

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To find: The mean, variance, and standard deviation for the function f(x)={18x if 0≤x≤130 otherwise.

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Chapter 11.3, Problem 3E

Chapter 11.3, Problem 5E

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Chapter 11 Solutions

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Ch. 11.1 - Evaluate the following, if it converges: 3dx(x1)2.Ch. 11.1 - Prob. 2MP Ch. 11.1 - Prob. 3MP Ch. 11.1 - Prob. 4MP Ch. 11.1 - Prob. 5MP Ch. 11.1 - Prob. 6MP Ch. 11.1 - Prob. 1ED Ch. 11.1 - Prob. 2ED Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E

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The mean, variance, and standard deviation for the function f ( x ) = { 18 x if 0 ≤ x ≤ 1 3 0 otherwise .

Solution Summary: The author calculates the mean, variance, and standard deviation for the function f(x) by using the above definition.

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To find: The mean, variance, and standard deviation for the function f(x)={18x if 0≤x≤130 otherwise.

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Chapter 11 Solutions