Explanation Given: Joint probability distribution: p ( x , y ) = { C y ; if 0 ≤ x ≤ 1 and x 2 ≤ y ≤ x 0 ; Otherwise Formula used: Probability for the given probability density function is given as: P ( ( X , Y ) ∈ D ) = ∬ D f X Y ( x , y ) d y d x Calculation: For the given function to be joint probability density function, we must have: ⇒ P ( X , Y ) = ∬ D f X Y ( x , y ) d y d x = 1 ⇒ P ( X , Y ) = ∫ 0 1 ∫ x 2 x C y d y d x = C ∫ 0 1 ∫ x 2 x y d y d x ⇒ P ( X , Y ) = C ∫ 0 1 [ y 2 2 ] x 2 x d x = C 2 ∫ 0 1 ( ( x ) 2 − ( x 2 ) 2 ) d x ⇒ P ( X , Y ) = C 2 ∫ 0 1 ( x 2 − x 4 ) d x = C 2 [ x 3 3 − x 5 5 ] 0 1 For joint probability density function, ⇒ P ( X , Y ) = C 2 [ 1 3 3 − 1 5

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 16.5, Problem 55E

To determine

The value of C such that the given function is joint probability density function.

The probability $P (Y \geq X^{\frac{3}{2}})$ .

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Chapter 16.5, Problem 54E

Chapter 16.5, Problem 56E

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Chapter 16 Solutions

CALCULUS (CLOTH)

Ch. 16.1 - Prob. 1PQ Ch. 16.1 - Prob. 2PQ Ch. 16.1 - Prob. 3PQ Ch. 16.1 - Prob. 4PQ Ch. 16.1 - Prob. 5PQ Ch. 16.1 - Prob. 6PQ Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E

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The value of C such that the given function is joint probability density function. The probability P ( Y ≥ X 3 2 ) .

Solution Summary: The author explains that the value of C is 15 and the required probability is P ( Y X 3 2 ) = 5 8

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The value of C such that the given function is joint probability density function.

The probability $P (Y \geq X^{\frac{3}{2}})$ .

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Chapter 16 Solutions

The value of C such that the given function is joint probability density function. The probability P ( Y ≥ X 3 2 ) .

Solution Summary: The author explains that the value of C is 15 and the required probability is P ( Y X 3 2 ) = 5 8

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The value of C such that the given function is joint probability density function. The probability P(Y≥X32).

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Chapter 16 Solutions

The value of C such that the given function is joint probability density function.

The probability $P (Y \geq X^{\frac{3}{2}})$ .