1.  Refer to Exercise 1.

a.  Find the conditional probability mass function pY|X (y|0).

b.  Find the conditional probability mass function pX|Y (x|1).

c.   Find the conditional expectation E(Y | X = 0).

d.  Find the conditional expectation E(X | Y = 1).

2.  Refer to Exercise 4.

a.  The total number of assemblies that fail to meet specifications is X + Y.

b.  Find µX+Y .

c.   Find σX+Y .

d.  Find P(X + Y = 3).

3.  Refer to Exercise 4.

a.  Find the conditional probability mass function pY|X (y | 1)

b.  Find the conditional probability mass function pY|X (y | 2)

c.   Find the conditional expectation E(Y | X = 1).

d.  Find the conditional expectation E(X | Y = 2).