Consider the random variable $N_n$ drawn from a Poisson distribution with intensity parameter $n$ so that $E(N_n)=n$.
Could you help me to show that $\frac{N_n}{n}\rightarrow_p 1$ as $n\rightarrow \infty$?
My doubts: I do not understand what happens to $N_n$ as $n\rightarrow \infty$. If I consider the probability distribution of the Poisson, when $n\rightarrow \infty$ the probability of observing $X_n=x$ goes to zero. Is this somehow related to the statement above?