Let [math]X[/math] be a random variable which is Poisson distributed with parameter [math]\lambda[/math]. Show that [math]E(X) = \lambda[/math]. Hint: Recall that

[[math]] e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \cdots\,. [[/math]]