7. A typist, on average, makes three typing errors in every two pages. If pages with more than two errors must be retyped, on average how many pages must she type to prepare a report of 200 pages? Assume that the number of errors in a page is a Poisson random variable. Note that some of the retyped pages should be retyped, and so on.

Hint: Find p, the probability that a page should be retyped. Let Xn be the number of pages that should be typed at least n times. Show that E(X1) = 200p, E(X2) =

200p2, . . . , E(Xn) = 200pn. The desired quantity is E

????P

∞ i

=1 Xi

, which can be calculated using relation (10.2).