## Find the marginal probability mass functions pX (x) and pY (y).

1.  A penny and a nickel are tossed. The penny has probability 0.4 of coming up heads, and the nickel has probability 0.6 of coming up heads. Let X = 1 if the penny comes up heads, and let X = 0 if the penny comes up tails. Let Y = 1 if the nickel comes up heads, and let Y = 0 if the nickel comes up tails.

a.  Find the probability mass function of X.

b.  Find the probability mass function of Y.

c.   Is it reasonable to assume that X and Y are independent? Why?

d.   Find the joint probability mass function of X and Y.

2.  Two fair dice are rolled. Let X represent the number on the first die, and let Y represent the number on the second die. Find µXY.

3.  A box contains three cards, labeled 1, 2, and 3. Two cards are chosen at random, with the first card being replaced before the second card is drawn. Let X represent the number on the first card, and let Y represent the number on the second card.

a.  Find the joint probability mass function of X and Y.

b.  Find the marginal probability mass functions pX (x) and pY (y).

c.    Find µX and µY .

d.  Find µXY .

e.   Find Cov(X,Y).

### 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….