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Suppose the number of phone calls made by the customers of a particular phone company in...

Suppose the number of phone calls made by the customers of a particular phone company in one hour is the random variable ? ~ ???????(?), where ? > ? is known. Let ?? be the length of the ? ?? phone call, for ? = ?, ?, ⋯ , ?. Assume the ?? ′? are independent of each other, and also independent of ?. Also assume that ?? ~ ???????????(?), for all ?, where ? > ? is known. Define ? = ∑ ?? ? ?=? , so that ? is the sum of the lengths of all the phone calls.

Find ?(?), the variance of ?.

Math   Statistics-And-Probability   
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