Poisson Random Variables

Question 1

p(x = k) in poisson random variables

Answer 1

e^λ * (λ^k)/k!

Question 2

what is the expected value of a poisson random variable

Answer 2

λ

Question 3

what is the variance in a poisson random variable

Answer 3

λ

Question 4

if there are 1.8 births per hour in a hospital

qhat is the probability of 4 births per hour

Answer 4

(e^-1.8) * ((1.8^4)/4!)

Question 5

what is expected value of

aX in poisson random variable

Answer 5

aE(X) = (a^2)*λ

Question 6

what is the variance of poisson random variable

aX

Answer 6

Var(aX) = a^2Var(X) = (a^2)*λ