115. Define a function p(x; , ) by p(x; , )
{ e e x
0, 1, 2, . . .

0 otherwise

a. Show that p(x; , ) satisfies the two conditions necessary for specifying a pmf, [Note: If a firm employs two typists, one of whom makes typographical errors at the rate of  per page and the other at rate per page and they each do half the firm’s typing, then p(x; , ) is the pmf of X
the number of errors on a randomly chosen page.]

b. If the first typist (rate ) types 60% of all pages, what is the pmf of X of part (a)?

c. What is E(X) for p(x; , ) given by the displayed expression?

d. What is 2 for p(x; , ) given by that expression?