## Find the marginal probability mass function pY (y).

1.  The number of bytes downloaded per second on an information channel has mean 10 5 and standard deviation 10 4 . Among the factors influencing the rate is congestion, which produces alternating periods of faster and slower transmission. Let X represent the number of bytes downloaded in a randomly chosen five-second period.

a.  Is it reasonable to assume that μx = 5 × 10 5?

b.  Explain. Is it reasonable to assume that ? Explain.

2.  Refer to Exercise 1.

a.  Find the marginal probability mass function pX (x).

b.  Find the marginal probability mass function pY (y).

c.   Find µX

d.  Find µY .

e.  Find σX .

f.     Find σY .

g.  Find Cov(X, Y).

h.  Find ρX,Y .

i.      Are X and Y independent? Explain.

### 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….