Use the formulas defining and 2 to show that the mean and th

Use the formulas defining and ² to show that the mean and the variance of the Poisson ditribution are both equal to.

Solution

As

u = np

sigma^2 = np(1-p)

As p<<1 for Poisson approximation, then 1 - p is approximately 1.

thus,

sigma^2 = (approx) np(1)

sigma^2 =(approx) np

Thus, as lambda = np, then for Poisson distribution,

mean = variance = lambda.