- 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.
- 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.