Problem 150SE

Refer to Exercise 5.149.

a Find E(Y2|Y1 = y1).

b Use Theorem 5.14 to find E(Y2).

c Find E(Y2) directly from the marginal density of Y2.

Reference

Let Y1 and Y2 have a joint density function given by

a Find the marginal density functions of Y1 and Y2.

b Find P(Y1 ≤ 3/4|Y2 ≤ 1/2).

c Find the conditional density function of Y1 given Y2 = y2.

d Find P(Y1 ≤ 3/4|Y2 = 1/2).

Solution:

Step 1 of 3:

Let Y1 and Y2 have a joint density function given by,

We have to find,

- E(Y2/Y1=y1).
- E(Y2).
- E(Y2) by using the marginal density of Y2.