Explanation Given: Joint probability distribution: p ( x , y ) = { C sin 2 ( 2 π l x ) sin 2 ( 2 π n y ) ; ( x , y ) ∈ R 0 ; Otherwise Where rectangle R is given by R = [ 0 , 1 ] × [ 0 , 1 ] 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 ∫ 0 1 To determine (b) The probability P ( 0 ≥ X ≥ 1 4 0 ≥ Y ≥ 1 8 ) .

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 16.5, Problem 57E

To determine

(a)

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

To determine

(b)

The probability $P (\begin{array}{l} 0 \geq X \geq \frac{1}{4} \\ 0 \geq Y \geq \frac{1}{8} \end{array})$ .

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Chapter 16.5, Problem 56E

Chapter 16.5, Problem 58E

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Chapter 16 Solutions

CALCULUS (CLOTH)

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(a) The value of constant C such that the given function is joint probability density function.

Solution Summary: The author determines the value of constant C such that the given function is joint probability density function.