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Computer response time is an important application of exponential distribution. Suppose that a study of a...

Computer response time is an important application of exponential distribution. Suppose that a study of a certain computer system reveals that the response time (X), in seconds, has an exponential distribution with a rate parameter θ. The study also showed that 90% of these computers respond within 5 seconds. a) Find the value of θ (round it to one decimal place) [4 points] b) What is the probability that a randomly selected computer will respond between 4 and 6 seconds? [2 points] c) If a random variable Y is defined as Y = 2X − 20 (i) Find the mean and variance of Y [2 points] (ii) Can Y be exponential random variable? Why? Briefly explain (no need of mathematical proof).

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