Answer to Question #206353 in Statistics and Probability for Tshimo

Question

If X is a random variable with Poisson distribution satisfying P(X=0) = P(X=1), calculate E(X). 

Answer 1

$P(X=x) = \frac{e^{-λ}λ^x}{x!} \\ x=0,1,2,… \\ E(x) = Var(x)= λ \\ P(X=0)=P(X=1) \\ \frac{e^{-λ}λ^0}{0!} = \frac{e^{-λ}λ^1}{1!} \\ λ=1 \\ E(x) = λ=1$