1)Customers enter a store according to a Poisson process of rate A = 6 per hour. Suppose it is known that but a single customer entered during
the first hour. What is the conditional probability that this person entered during the first fifteen minutes?
2Let {X(t); t >= 0) be a Poisson process having rate parameter lambda= 2. Determine the numerical values to two decimal places for the following
probabilities:
(a) Pr{X(1) <= 2}.
(b) Pr{X(1) = 1 and X(2) = 3).
(c) Pr{X(1) >= |X(1) >= 1)
3)Let {X(t); t >= 0) be a Poisson process having rate parameter lambda= 2.
Determine the following expectations:
(a) E[X(2)].
(b) E[{X(1)}^2]
(c) E[X(1) X(2)].