Problem 58E

Suppose that the random variables Y1 and Y2 have joint probability density function, f (y1, y2), given by (see Exercises 5.14 and 5.32)

Show that Y1 and Y2 are dependent random variables.

Reference

Exercise 5.32 Suppose that the random variables Y1 and Y2 have joint probability density function, f (y1, y2), given by (see Exercise 5.14)

a Show that the marginal density of Y1 is a beta density with α = 3 and β = 2.

b Derive the marginal density of Y2.

c Derive the conditional density of Y2 given Y1 = y1.

d Find P(Y2 < 1.1|Y1 = .60).

Reference

Suppose that the random variables Y1 and Y2 have joint probability density function f (y1, y2) given by

a Verify that this is a valid joint density function.

b What is the probability that Y1 + Y2 is less than 1?

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