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.

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