Explanation Given information: The density function of a random variable X is f ( x ) = 1 4 , 1 ≤ x ≤ 5 . Formula used: 1) E ( X ) = ∫ A B x f ( x ) d x . 2) Var ( X ) = ∫ A B x 2 f ( x ) d x − [ E ( X ) ] 2 . Calculation: A random variable X with the density function f ( x ) = 1 4 , 1 ≤ x ≤ 5 1) E ( X ) = ∫ A B x f ( x ) d x . Plug limits A = 1 , B = 5 , and f ( x ) = 1 4 in the expected value formula, E ( X ) = ∫ 1 5 1 4 x d x Using the power rule of integration, ⇒ E ( X ) = x 2 8 | 1 5 = 5 2 8 − 1 2 8 = 3 2) Var ( X ) = ∫ A B x 2 f ( x ) d x − [ E ( X ) ] 2

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Chapter 12.3, Problem 3E

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To calculate: The expected value E(X) and variance Var(X) with the density function f(x)=14 , 1≤x≤5.

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Chapter 12.3, Problem 2E

Chapter 12.3, Problem 4E

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The expected value E ( X ) and variance Var ( X ) with the density function f ( x ) = 1 4 , 1 ≤ x ≤ 5 .

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To calculate: The expected value E(X) and variance Var(X) with the density function f(x)=14 , 1≤x≤5.

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Chapter 12 Solutions