Question

If a random variable X follows Poisson distribution sucli that P(X = 1) = P(X = 2), find:
(a) the mean and
(b) P(X = 0). [Given: e^-2 = 0.1353)

Answer 1

P(X = x) = P(x) = `("e"^(-"m") . "m"^2)/("x"!)` , 

Given P(X= l)= P(X= 2) 

`therefore ("e"^(-"m") . "m"^1)/(1!) = ("e"^(-"m") . "m"^2)/(2!)`

⇒  m = 2

P[X = 0] =  `("e"^(-2) . 2^2)/(0!)`

             = `("e"^(-2) . 1)/(1)`

            = 0.1353