Question

For a Poisson distributed random variable X, P(X = 4) = P(X = 5).Find the mean
and variance of the distribution.

Answer 1

(\tag{hi}(\lambda^{4}*e^{-4})/4!=(\lambda^{5}*e^{-5})/5! -> 5!*\lambda^{4}=4!*\lambda^{5} -> \lambda=5

$E(X)=Var(X)=\lambda=5$