Let Y1 and Y2 have joint density function first encountered in Exercise 5.7: f (y1, y2)
Chapter 5, Problem 5.25(choose chapter or problem)
Let Y1 and Y2 have joint density function first encountered in Exercise 5.7: f (y1, y2) = e(y1+y2) , y1 > 0, y2 > 0, 0, elsewhere. a Find the marginal density functions for Y1 and Y2. Identify these densities as one of those studied in Chapter 4. b What is P(1 < Y1 < 2.5)? P(1 < Y2 < 2.5)? c For what values of y2 is the conditional density f (y1|y2) defined? d For any y2 > 0, what is the conditional density function of Y1 given that Y2 = y2? e For any y1 > 0, what is the conditional density function of Y2 given that Y1 = y1?f For any y2 > 0, how does the conditional density function f (y1|y2) that you obtained in part (d) compare to the marginal density function f1(y1) found in part (a)? g What does your answer to part (f) imply about marginal and conditional probabilities that Y1 falls in any interval?
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