Let X denote the data transfer time (ms) in a grid computing system (t
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Answered question
2021-11-28
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,” 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?
Answer & Explanation
Blanche McClain
Beginner2021-11-29Added 15 answers
The random variable X represents the data transfer time in a grid computing system.
It is given that the random variable X has a gamma distribution with mean value 37.5 ms and standard deviation 21.6.
The mean and variance of a gamma variate with parameters
Thus, the values of
Consider the ratio,
Step 2
The value of
Part b
Computing the probability that data transfer time exceeds 50ms:
z-score:
If a random variable X has a distribution with
Observe the value in the z-table corresponding to the
The area for the left side of
Subtract 0.7190 from 1 to evaluate the total area of the
Probability
Therefore the probability that data transfer time exceeds 50 ms is 0.281
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