Explanation Proof: The uniform probability density function is, f ( x ) = { 1 b − a if a ≤ x ≤ b 0 otherwise . The variance can be calculated by using, V ( X ) = ∫ − ∞ ∞ x 2 f ( x ) d x − μ 2 (1) Compute the value of ∫ − ∞ ∞ x 2 f ( x ) d x for the interval [ a , b ] . ∫ − ∞ ∞ x 2 f ( x ) d x = ∫ − ∞ a x 2 f ( x ) d x + ∫ a b x 2 f ( x ) d x + ∫ b ∞ x 2 f ( x ) d x = 0 + ∫ a b x 2 ( 1 b − a ) d x + 0 ( ∵ x < a = 0 x > b = 0 ) = 1 b − a [ x 3 3 ] a b = 1 b − a [ b 3 3 − a 3 3 ] On further simplification

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Chapter 11.4, Problem 62E

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To show: The variance of uniform probability density function is V(X)=(b−a)212.

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Chapter 11.4, Problem 61E

Chapter 11.4, Problem 63E

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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 variance of uniform probability density function is V ( X ) = ( b − a ) 2 12 .

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