Explanation Given: The cumulative distribution function is, F ( x ) = { 0 if x < 1 x 2 − 1 2 if 1 ≤ x ≤ 3 1 if x > 3 } . Formula used: Probability density function : If F ( x ) is a cumulative distribution function associated with the probability density function f ( x ) , then f ( x ) = F ′ ( x ) . Calculation: Obtain the probability density function by computing derivative of cumulative distribution function over the given interval. Calculate the probability density function for x < 1 as follows. f ( x ) = d d x ( F ( x ) ) = d d x ( 0 ) ∵ F ( x ) = 0 for x < 1 = 0 That is, f ( x ) = 0 for x < 1 . Calculate the probability density function for 1 < x < 3 as follows

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Chapter 11.2, Problem 50E

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To find: The probability density function f(x) associated with the cumulative distribution function F(x).

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Chapter 11.2, Problem 49E

Chapter 11.2, Problem 51E

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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 probability density function f ( x ) associated with the cumulative distribution function F ( x ) .

Solution Summary: The author calculates the probability density function for x1 by computing derivative of cumulative distribution function over the given interval.

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To find: The probability density function f(x) associated with the cumulative distribution function F(x).

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Chapter 11 Solutions