五、Suppose $X_1, X_2, \ldots, X_n$ are independent random variables and follow Poisson distribution with mean $\lambda$. Please use moment generating function to show that $\overline{X} = \sum X_i / n$ converges in probability to $\lambda$. (Hint: The distribution of $\overline{X}$ degenerates to a constant random variable.) (10%)