Explanation Given information: The probability density function is p ( x ) = C 1 − x 2 on ( − 1 , 1 ) . Formula used: If p is a probability density function for X , then it is a continuous function such that P ( a ≤ X ≤ b ) = ∫ a b p ( x ) d x . Also a probability function p ( x ) must satisfy two conditions such that p ( x ) ≥ 0 for all x ∫ − ∞ ∞ p ( x ) d x = 1 ∫ 1 − x 2 d x = 1 2 ( sin − 1 x + x 1 − x 2 ) + C Calculation: A probability density function p ( x ) must satisfy ∫ − ∞ ∞ p ( x ) d x = 1 . p ( x ) = C 1 − x 2 (Given) So, ∫ − ∞ ∞ p ( x ) d x = 1 ⇒ ∫ − 1 1 C 1 − x 2 d x = 1 ⇒ C ∫ − 1 1 1 − x 2 d x = 1 ⇒ C ∫ − 1 1 1 − x 2 d x = 1 ⇒ C 1 2 [ sin − 1 x + x 1 − x 2 ] − 1 1 = 1 ⇒ C 2 [ ( sin − 1 1 + 1 1 − 1 ) − ( sin − 1 ( − 1 ) <

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 9.1, Problem 7E

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To find: The constant C and also compute the value of P(−12≤X≤1) .

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Chapter 9.1, Problem 6E

Chapter 9.1, Problem 8E

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Chapter 9 Solutions

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Ch. 9.1 - Prob. 1PQ Ch. 9.1 - Prob. 2PQ Ch. 9.1 - Prob. 3PQ Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E

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The constant C and also compute the value of P ( − 1 2 ≤ X ≤ 1 ) .

Solution Summary: The author calculates the probability density function p(x)=Csqrt1-x2 on (-1,1).

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To find: The constant C and also compute the value of P(−12≤X≤1) .

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Chapter 9 Solutions