Question

please answer c and d part
The number of network errors happened in a day on a local area network (LAN) is distributed as a
Poisson random variable. The mean number of network errors happened in a day is 3.4.
(a) What is the probability that there are more than four network errors in a day?
(b) What is the probability that there are exactly a total of 8 network errors in two consecutive days?
(c) There is a penalty system apply for the service provider according to the following descriptions:
(i) There is a penalty of $20000 if there are more than 4 days in a week (Sunday to Saturday)
that there are more than four network errors in a day.
(ii) There is a penalty of $13000 if there are 2 to 4 days in a week (Sunday to Saturday) that there
are more than four network errors in a day.
(iii) There is no penalty if there is less than 2 days in a week (Sunday to Saturday) that there are
more than four network errors in a day.
Tabulate the probability distribution function of the weekly penalty paid by the service provider due
to the network errors. (Present the table in this page and the calculation in the next page).
(d) Hence, find the expectation and standard deviation of the weekly penalty paid by the service provider
due to the network errors.

Answer 1

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