In Exercise 5.6, we assumed that if a radioactive particle is randomly located in a
Chapter 5, Problem 5.24(choose chapter or problem)
In Exercise 5.6, we assumed that if a radioactive particle is randomly located in a square with sides of unit length, a reasonable model for the joint density function for Y1 and Y2 is f (y1, y2) = $ 1, 0 y1 1, 0 y2 1, 0, elsewhere. a Find the marginal density functions for Y1 and Y2. b What is P(.3 < Y1 < .5)? P(.3 < Y2 < .5)? c For what values of y2 is the conditional density f (y1|y2) defined? d For any y2, 0 y2 1 what is the conditional density function of Y1 given that Y2 = y2? e Find P(.3 < Y1 < .5|Y2 = .3). f Find P(.3 < Y1 < .5|Y2 = .5). g Compare the answers that you obtained in parts (a), (d), and (e). For any y2, 0 y2 1 how does P(.3 < Y1 < .5) compare to P(.3 < Y1 < .5|Y2 = y2)?
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