Question

If X is a Poisson variate and p(X = 3) > p(X
= 2) then find the minimum value of mean

Answer 1

P(x=3)>p(x=2)

(e^-lamda d^2)/3! > (e^-lamda lamda^2)/ 2!

henece d= 3 

mean = 3

Answer 2

let α be the mean
$\frac{e^{- \alpha } \alpha^3 }{3!}> \frac{e^{- \alpha } \alpha^2}{2!} \\ a>3$
so mean value of α=3(minimum value)