A factory encounters power outages which lead to loss of its profits. The number of power...
A factory encounters power outages which lead to loss of its profits. The number of power outages in one year is a μ=4-Poisson random variable. Suppose the factory has some backup products which could avoid any loss for the first outage, but for every outage after that, the factory would have a loss of $8,0008,000. Find out what will be the expected loss of that factory in one year.
Homework Answers
We are given that outgage follow Poisson distribution with
parameter 
=4
So Let x denotes number of outgages E(x)=4
Let L denotes loss so L=$80008000x
E(L)=$80008000E(x)=80008000(4)
= $320,032,000
The average annual number of power outages is 4, with the company having backup for the initial outage. Consequently, the average number of power outages without backup in a year is 3.
The cost of loss per power outage is $8,000.
Hence, the anticipated loss amounts to 3 times $8,000, which equals $24,000.
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