A small publisher employs two typesetters. The number of errors (in one book) made by the first typesetter has a Poisson distribution mean μ₁, the number of errors made by the second typesetter has a Poisson distribution with mean μ₂, and each typesetter works on the same number of books. Then if one such book is randomly selected, the function

gives the pmf of X = the number of errors in the selected book.

a. Verify that p(x; μ₁, μ₂) is a legitimate pmf ( ≥ 0 and sums to 1).
b. What is the expected number of errors in the selected book?
c. What is the standard deviation of the number of errors in the selected book?
d. How does the pmf change if the first typesetter works on 60% of all such books and the second typesetter works on the other 40%?

Transcribed Image Text:

p(x; μ₁₂ µ₂) = .5e-¹. -Se-mi x! x = 0, 1, 2, ... M₂ x! +.5e-th₂.