Explanation Given information: The given probability density function is p ( x ) = C 1 − x 2 on ( − 1 , 1 ) . Given probability is P ( − 1 2 ≤ X ≤ 1 2 ) . Formula used: A function p ( x ) will be a probability density function of a random variable X , if it satisfies the following condition. 1). p ( x ) ≥ 0 for all x ∈ R 2). ∫ − ∞ ∞ p ( x ) d x = 1 3). P ( a ≤ X ≤ b ) = ∫ a b p ( x ) d x = F ( b ) − F ( a ) such that F is an antiderivative of p . Calculation: Let us consider the given probability density function. p ( x ) = C 1 − x 2 Now p ( x ) should satisfy the condition ∫ − ∞ ∞ p ( x ) d x = 1 . ∫ − ∞ ∞ p ( x ) d x = 1 ∫ − 1 1 C 1 − x 2 d x = 1 C ∫ − 1 1 1 1 − x 2 d x = 1 C [ sin − 1

4th Edition

ISBN: 9781319055905

Author: FRANZOSA

Publisher: VST

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Chapter 8.1, Problem 3E

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The constant C such that given p(x) is a probability density function. Compute the value of P(−12≤X≤12).

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Chapter 8.1, Problem 2E

Chapter 8.1, Problem 4E

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Chapter 8 Solutions

EBK CALCULUS: EARLY TRANSCENDENTALS

Ch. 8.1 - Prob. 1PQ Ch. 8.1 - Prob. 2PQ Ch. 8.1 - Prob. 3PQ Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E

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The constant C such that given p ( x ) is a probability density function. Compute the value of P ( − 1 2 ≤ X ≤ 1 2 ) .

Solution Summary: The author calculates the value of p(x) based on the given probability density function.

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To find:

The constant C such that given p(x) is a probability density function. Compute the value of P(−12≤X≤12).

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Chapter 8 Solutions

The constant C such that given p ( x ) is a probability density function. Compute the value of P ( − 1 2 ≤ X ≤ 1 2 ) .

Solution Summary: The author calculates the value of p(x) based on the given probability density function.

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To find: The constant C such that given p(x) is a probability density function. Compute the value of P(−12≤X≤12).

Want to see the full answer?

Chapter 8 Solutions

To find:

The constant C such that given p(x) is a probability density function. Compute the value of P(−12≤X≤12).