6 Let X be a Poisson random variable with parameter 5 and

6. Let X be a Poisson random variable with parameter ? = 5, and let Y = min(X, 12).
(a) What is the p.m.f. of X?
(b) What is the mean of X?
(c) What is the variance of X?
(d) What is the p.m.f. of Y ?
(e) Compute E[Y ].

Solution

probability mass function of X = 5^k/k! { e ^ (-5)} k is all integers greater and equal to 0

mean = parameter = 5

variance = parameter = 5

probability mass function of Y = SIGMA k = 0 to 12 [ 5^k/k! { e ^ (-5)} ] ---- where k is all integers greater and equal to 0

E[Y] = 5