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Lelu
1 month ago
8

The manager of an industrial plant is planning to buy a new machine. For each day’s operation, the number of repairs X, that the

machine needs is a Poisson random variable with mean 0.96 repairs per day. The daily cost of operating the machine is C = 160 + 40X2 . Find the expected value of the daily cost of operating the machine.
Mathematics
1 answer:
zzz [12.3K]1 month ago
5 0

Response:  The expected daily cost of operating the machine is 235.264.

Step-by-step breakdown:

The given average is

E[x]= 0.96 repairs per day

And Var[x] = 0.96 repairs per day.

C=160+40x^2

E[c]=160+40E[x^2]\\\\E[c]=160+40(Var[x]+(E[x])^2)\\\\E[c]=160+40(0.96+0.96^2)\\\\E[c]=235.264

Thus, the expected daily cost of running the machine amounts to 235.264.

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3 months ago
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2 months ago
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