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 \( \alpha \) and \( \beta \)? (Round your answers to four decimal places.)\[ \alpha = \text{\_\_\_\_} \]\[ \beta = \text{\_\_\_\_} \]**(b)** What is the probability that data transfer time exceeds 48 ms? (Round your answer to three decimal places.)\[ \text{\_\_\_\_} \]**(c)** What is the probability that data transfer time is between 48 and 72 ms? (Round your answer to three decimal places.)\[ \text{\_\_\_\_} \]

Answered: Let X denote the data transfer time…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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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, "t). (a) What are the values of a and 8? (Round your answers to four decimal places.) a = 3.0141 B = 12.4416 (b) what is the probability that data transfer time exceeds 51 ms? (Round your answer to three decimal places.) 0.265 (c) What is the probability that data transfer time is between 51 and 79 ms? (Round your answer to three decimal places.) 0.210 You may need to use the appropriate table in the Appendix of Tables to answer this question.

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