1. When a program is submitted to the computer in a time-sharing system, it is processed on a space-available basis. Past experience shows that a program submitted to one such system is accepted for processing within one minute with probability.
2. Assume that during the course of a day five programs are submitted with enough time between submissions to ensure independence. Let X denote the number of programs accepted for processing within one minute.
(a) Find E[X] and Var X.
(b) Find the probability that none of these programs will be accepted for processing within one minute. (c) Five programs are submitted on each of two consecutive days. What is the probability that no programs will be accepted for processing within one minute during this two-day period?