1. Consider the function f ( x ) = cx3 for x = 1, 2, 3, 4; where c is a constant. Let X be a discrete random variable with probability function f (x).
(a) Determine the value of c that makes f ( x ) a probability function.
(b) Find P( X 2).
(c) Find P(2 X ::; 3).
(d) Find E[X].
(e) Find Var[X].
2. Defects on computer disks are known to occur at a rate of two defects per (mm) 2 and they occur according to a Poisson model.
(a) Find the probability that at least one defect will be found if 1 (mm) 2 is examined.
(b) Find the probability of less than two defects if 1 (mm)2 is examined.