Explanation Given information: f ( x ) = 3 2 x − 3 4 x 2 , 0 ≤ x ≤ 2 . Explanation: f ( x ) = 3 2 x − 3 4 x 2 ≥ 0 for all 0 ≤ x ≤ 2 The given function is probability density function if it satisfies below condition. ∫ − ∞ ∞ f ( x ) d x = 1 . Substitute given function f ( x ) = 3 2 x − 3 4 x 2 , 0 ≤ x ≤ 2 ∫ − ∞ ∞ f ( x ) d x = ∫ 0 2 ( 3 2 x − 3 4 x 2 ) d x Using the sum rule of integration ∫ f ( x ) ± g ( x ) d x = ∫ f ( x ) d x ± ∫ g ( x ) d x ⇒ ∫ 0 2 ( 3 2 x − 3 4 x 2 ) d x = ∫ 0 2 3 2 x d x − ∫ 0 2 3 4 x 2 d x Take the constant 3 2 and 3 4 <

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Chapter 12.2, Problem 6E

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Whether, the function f(x)=32x−34x2, 0≤x≤2 is a probability density function or not.

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Chapter 12.2, Problem 5E

Chapter 12.2, Problem 7E

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Whether, the function f ( x ) = 3 2 x − 3 4 x 2 , 0 ≤ x ≤ 2 is a probability density function or not.

Solution Summary: The author explains that the given function is a probability density function if it satisfies below condition.

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Whether, the function f(x)=32x−34x2, 0≤x≤2 is a probability density function or not.

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Chapter 12 Solutions