Let X denote the data transfer time (ms) in a grid computingsystem (the time required for data transfer between a “worker” computer and a “master” computer.Suppose that X has a gamma distribution with meanvalue 37.5 ms and standard deviation 21.6 (suggested bythe article “Computation Time of Grid Computingwith Data Transfer Times that Follow a GammaDistribution,” Proceedings of the First InternationalConference on Semantics, Knowledge, and Grid, 2005).a. What are the values of a and b?b. What is the probability that data transfer time exceeds50 ms?c. What is the probability that data transfer time isbetween 50 and 75 ms?
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!
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
value
the article “Computation Time of Grid Computing
with Data Transfer Times that Follow a Gamma
Distribution,” Proceedings of the First International
Conference on Semantics, Knowledge, and Grid, 2005).
a. What are the values of a and b?
b. What is the probability that data transfer time exceeds
50 ms?
c. What is the probability that data transfer time is
between 50 and 75 ms?
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