The number of bytes downloaded per second on an information channel has mean 
and standard deviation 
. 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 
? Explain.
b. Is it reasonable to assume that 
? Explain.
(a) Yes. Let 
denote the number of bytes downloaded in the ith second. The total number of bytes is
. The mean of the total number is the sum of the five means, each of which is equal to 
.
(b) No.
are not independent, so the standard deviation of the sum depends on the covariances between the 
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