Need all parts, a,b,and c Let X denote the data transfer time (ms) in a grid computing system (the time required for data transfer between a "worker" computer and a "master" computer). Suppose that X has a gamma distribution with mean value 37.5 ms and standard deviation 21.6 (suggested by the article "Computation Time of Grid Computing with Data Transfer Times that Follow a Gamma Distribution,"†). (a) What are the values of α and β? (Round your answers to four decimal places.) (b) What is the probability that data transfer time exceeds 47 ms? (Round your answer to three decimal places.) (c) What is the probability that data transfer time is between 47 and 76 ms? (Round your answer to three decimal places.)
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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