(a) Explanation Given information: The function f ( x ) = 30 x 2 ( 1 − x ) 2 for 0 ≤ x ≤ 1 . The function f ( x ) = 0 for all other values of x . Hence, f ( x ) ≥ 0 for all x . The region lies between a = 0 and b = 1 . Explanation: Show the function as follows: f ( x ) = 30 x 2 ( 1 − x ) 2 (1) Modify Equation (1). f ( x ) = 30 x 2 ( 1 + x 2 − 2 x ) = 30 x 2 + 30 x 4 − 60 x 3 = 30 x 4 − 60 x 3 + 30 x 2 Apply probability density function as follows: (A) The probability density function f of a random variable X satisfies the condition f ( x ) ≥ 0 for all x (b) To determine To calculate: The value of P ( X ≤ 1 3 ) .

8th Edition

ISBN: 9781305266636

Author: James Stewart

Publisher: Cengage Learning

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Chapter 8.5, Problem 3E

(a)

To determine

To verify: The function f is a probability density function.

(b)

To determine

To calculate: The value of P(X≤13) .

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Chapter 8.5, Problem 2E

Chapter 8.5, Problem 4E

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To verify: The function f is a probability density function.

Solution Summary: The author explains the probability density function of a random variable X satisfies the condition f(x)ge 0 for all x.

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To verify: The function f is a probability density function.

To calculate: The value of P(X≤13) .

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Chapter 8 Solutions