Customers arrive at a service facility according to a Poisson process with an average rate of 5 per hour. Find

(a) The probabilities that (i) during 6 hours no customers will arrive, (ii) at most, twentyfive customers will arrive;

(b) The probabilities that the waiting time between the third and the fourth customers will be (i) greater than 30 min., (ii) equal to 30 min., (iii) greater than or equal to 30 min.;

(c) The probability that after the first customer has arrived, the waiting time for the fifth customer will be greater than an hour;

(d) For the same waiting time, its expected value and standard deviation.