Question: there are three questions. Problem 1. (Random Variables) Prove that the mean and standard deviation of the exponential distribution are equal. Problem 2. (Queueing Theory)

there are three questions. Problem 1. (Random

there are three questions.

Problem 1. (Random Variables) Prove that the mean and standard deviation of the exponential distribution are equal. Problem 2. (Queueing Theory) The time between failures of a Kencore refrigerator is known to be exponential with mean value 9000 hrs (about 1 year of operation), and the company issues a 1-year warranty on the refrigerator. What are the chances that a breakdown repair will be covered by the warranty? Problem 3. (Queueing Theory) The time between arrivals at the game room in the student union is exponential, with mean 10 minutes. (a) What is the arrival rate per hour? (b) What is the probability that no students will arrive at the game room during the next 15 minutes (c) What is the probability that at least one student will visit the game room during the next 20 minutes

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