A study of a large number of towns with approximately 100,000 people estimates the probability that one will have a certain number X of pita restaurants. None of the towns had more than 5. They construct a table of the probability distribution function p(x) = P(X = x) and the cumulative distribution function F(x) = P(X ≤ x) for the number of pita restaurants in a town.
A student shows you a paper copy of these results. Unfortunately, he was caught in a snow shower crossing campus, and only part of the table is readable:

0 1 2 3 4 5
p(x) .20 .14
F(x) .33 .71 .94

(a) Fill in the damaged parts of the table. What is P(1 (b) Calculate the expected number of knots in a beam, E(X).
(c) Write down the probability generating function, πₓ(q) = E(qˣ).
Use it to answer the following question: if 94% of all pita restaurants do takeout, what is the probability that all the pita restaurants in a given town do takeout? (Assume they do not consult each other.)