Let Y1 and Y2 have the joint probability density function given by f (y1, y2) = ky1 y2

Chapter 5, Problem 5.8

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QUESTION:

Let Y1 and Y2 have the joint probability density function given by f (y1, y2) = ky1 y2, 0 y1 1, 0 y2 1, 0, elsewhere. a Find the value of k that makes this a probability density function. b Find the joint distribution function for Y1 and Y2. c Find P(Y1 1/2, Y2 3/4).

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QUESTION:

Let Y1 and Y2 have the joint probability density function given by f (y1, y2) = ky1 y2, 0 y1 1, 0 y2 1, 0, elsewhere. a Find the value of k that makes this a probability density function. b Find the joint distribution function for Y1 and Y2. c Find P(Y1 1/2, Y2 3/4).

ANSWER:

Step 1 of 4

Given that  and  have the joint probability density function given by,

 Otherwise

 

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