The number of telephone calls arriving at an exchange during any given minute between noon and 1:00 P.M. on a weekday is a random variable with the following probability distribution.,X P(x),0 ………… 0.3,1 ………… 0.2,2 ………… 0.2,3 ………… 0.1,4 ………… 0.1,5 ………… 0.1,a. Verify that P(x) is a probability distribution.,b. Find the cumulative distribution function of the random variable.,c. Use the cumulative distribution function to find the probability that between 12:34 and 12:35 P.M. more than two calls will arrive at the exchange.

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