A main-frame computer, that serves a network of terminals, is known to crash after an average of 44 hours. Suppose that you model the probability of failure of the main-frame by an exponential density function with a mean of 44 hours. (a) Using the exponential density function model, calculate the probability the mainframe will crash within the first 22 hours. Give your answer in exact (not decimal) form. (b) Calculate the median of the lifetime of the main-frame computer. Give your answer in exact (not decimal) form.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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