Next week, the number of projects that will require you to work overtime has a Poisson distribution with mean 1. For each project, the distribution of the number of overtime hours in the week is the following:

x	f(x)
5	0.2
10	0.3
20	0.5

The number of projects and number of overtime hours are independent. You will get paid for overtime hours in excess of 10 hours in the week. (For example, if 3 projects each require 5 overtime hours, you will get paid for (3)(5) -10 = 5 hours of overtime.)

(a) What is the probability that you won't have to work any overtime hours next week?

(b) What is the probability that you will have to work a total of 5 overtime hours next week? 

(c) What is the probability that you will have to work a total of 10 overtime hours next week? 

 (d) What is the expected number of overtime hours you will have to work next week?  

(e) What is the expected number of overtime hours for which you will not get paid next week? 

(f) What is the expected number of overtime hours for which you will get paid next week? 

 

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