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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.

Respuesta :

Answer:  Expected value of the daily cost of operating the machine is 235.264.

Step-by-step explanation:

Since we have given that

E[x]= 0.96 repairs per day

And Var[x] = 0.96 repairs per day.

[tex]C=160+40x^2[/tex]

[tex]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[/tex]

Hence, Expected value of the daily cost of operating the machine is 235.264.

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