## Find the conditional probability mass function pY\X (y | 4)

1.  Refer to Exercise 4. Assume that the cost of repairing an assembly whose clearance is too little is \$2, and the cost of repairing an assembly whose clearance is too much is \$3.

a.  Express the total cost of repairs in terms of X and Y.

b.  Find the mean of the total cost of repairs.

c.   Find the standard deviation of the total cost of repairs.

2.   Refer to Exercise 9.

a.  Find µX+Y

b.  . Find σX+Y .

c.   Find P(X + Y = 5)

3.  Refer to Exercise 9.

a.   Find the conditional probability mass function pY\X (y | 4)

b.   Find the conditional probability mass function pY\X (x | 3)

c.    Find the conditional expectation E(Y | X = 4).

d.  Find the conditional expectation E(X | Y = 3).

### What is the probability that the parcel was shipped express and arrived the next day?

1.  In a lot of n components, 30% are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective,….

### Given that the test is positive, what is the probability that the person has the disease?

1.  Refer to Exercise 28. Assume that both inspectors inspect every item and that if an item has no flaw, then neither inspector will detect a flaw. a.  Assume that….

### If a man tests negative, what is the probability that he actually has the disease?

1.  Refer to Example 2.26. a.  If a man tests negative, what is the probability that he actually has the disease? b.  For many medical tests, it is standard procedure….