A First Course in Probability (10th Edition)
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ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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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, "+").
**(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.)
\[
\text{\_\_\_\_}
\]](https://content.bartleby.com/qna-images/question/390df6bc-8765-4adb-882a-689888791ad2/f4acc721-f52c-4f3e-84dd-8bd93e7cfb33/9a45w3v_processed.png)
Transcribed Image Text: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.)
\[
\text{\_\_\_\_}
\]
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