If Y is a Poisson rv with lambda16 what are EY and VY Now co

If Y is a Poisson rv with lambda=16, what are E(Y) and V(Y)? Now consider 40 random variables, independent and identically distributed to Y. Using the CLT, compute the probability that the average of these 40 r.v.’s is between 15 and 17.

Solution

E(Y)=V(Y) =lambda = 16.

for lambda 16 from poission table P(Y>=15 and Y<=17) = P(Y<=17) - P(Y<=15) = 0.6593 - 0.4667 = 0.1926.

Refer http://stattrek.com/online-calculator/poisson.aspx for poission table calculations.