Show All Work 5. Suppose we have three types of GPU's: A, B, C - at a super-computing facility. The time takenby each of the GPU: A, B, C - to perform a given task is model by exponential distributionsExp(A4), Exp(λB = 1), Exp(Ac = 0.2) respectively.Additionally, there are a total 10 GPUs, 2 of which are of Type A, 5 are of Type B, and theremaining are of Type C.When a task arrrives at the facility, we randomly assing the task to one of the 10 GPUs.(a) What is the probability that a task arriving at the computing center will be finished in 2hrs?(b) What is the probability that a task arriving at the center will take between 1 and 4 hours?(c) What is the expected amount of time to finish a task arriving at the center?Show the setup and all work.

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Answered: 5. Suppose we have three types of…

Linear Algebra: A Modern Introduction

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ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 2EQ: 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed...

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5. Suppose we have three types of GPU's: A, B, C - at a super-computing facility. The time taken
by each of the GPU: A, B, C - to perform a given task is model by exponential distributions
Exp(A4), Exp(λB = 1), Exp(Ac = 0.2) respectively.
Additionally, there are a total 10 GPUs, 2 of which are of Type A, 5 are of Type B, and the
remaining are of Type C.
When a task arrrives at the facility, we randomly assing the task to one of the 10 GPUs.
(a) What is the probability that a task arriving at the computing center will be finished in 2
hrs?
(b) What is the probability that a task arriving at the center will take between 1 and 4 hours?
(c) What is the expected amount of time to finish a task arriving at the center?
Show the setup and all work.

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