For a Poisson variable $X$, $P(X = 1) = P(X = 2)$. What is its mean?

Explanation

1. 01

   $e^{-\lambda}\lambda = \frac{e^{-\lambda}\lambda^{2}}{2}$.

2. 02

   Dividing by $e^{-\lambda}\lambda$: $1 = \frac{\lambda}{2}$, so $\lambda = 2$, which is the mean.