Explanation Given: The function f ( x ) = 3 8 x 2 and specified interval 0 ≤ x ≤ 2 . Definition used: “A probability density function of a random variable X in an interval I , where I may be bounded or unbounded is a nonnegative function f having the following properties. 1. The total area of the region under the graph of f is equal to 1. 2. The probability that an observed value of the random variable X lies in the interval [ a , b ] is P ( a ≤ X ≤ b ) = ∫ a b f ( x ) d x .” Proof: The given function f ( x ) = 3 8 x 2 is non negative on [ 0 , 2 ] . The total area of the region under the graph of f is computed follows, Integrate the function f ( x ) = 3 8 x 2 on [ 0 , 2 ] and obtain the area

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ISBN: 9781337825597

Author: Tan

Publisher: INTER CENG

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Chapter 10.1, Problem 3E

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To show: The function is a probability density function on the specified interval.

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Chapter 10.1, Problem 2E

Chapter 10.1, Problem 4E

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Chapter 10 Solutions

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The function is a probability density function on the specified interval.

Solution Summary: The author explains that the given function is a probability density function on the specified interval. The total area of the region under the graph of f is equal to 1.

To show: The function is a probability density function on the specified interval.

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Chapter 10 Solutions