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Telephone calls to the general office of a university department on a working day follows a...

Telephone calls to the general office of a university department on a working day follows a Poisson process with the rate of occurrence being 2 every 30 minutes. Let X denote the waiting time (in minutes, counted from 10 am) until the first call that arrives.

(a) What is the pdf of X? Name the pdf if it has a name.

(b) Find P(X > 10).

(c) Find P(X > 15|X > 0).

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