A book is sent to be printed by one out of three printers:

• Printer 1
• Printer 2
• Printer 3

For Printer j, probability distribution of the number of errors ~ Poisson with λj for j = 1, 2, 3

Each printer is equally likely to be selected to the printing job

Let N be the number of printing errors

1. Find PMF of N, E(N) and Var(N)
2. If there are n printing errors (N=n)
   Find P(Printer j was selected for the job (N=n), j= 1,2,3)
3. If
   λ1 < λ2 < λ3 and N=0

Which printer was most likely to have been selected? Explain why

4. If
   λ1 < λ2 < λ3 and N is large
   Which printer was most likely to have been selected? Explain why