I am trying to use Markov's inequality to show that for a sequence of positive random variables $X_1, X_2, ....$ with values in $N={0,1,2,...}$ and $lim_{i\rightarrow\infty}E[X_i]=0$, it holds that $lim_{i\rightarrow\infty}P[X_i=0]=1$.

Intuitively, I understand this concept due to the law of large numbers, since as $i$ approaches infinity the expected value converges to the true mean 0, and the probability that $X_i$ equals the true mean converges to 1.

However, I am stumped as to how to use Markov's Inequality, $P(X\geq c)=E(X)/c$, to prove this. Any help is appreciated.

I am trying to use Markov's inequality to show that for a sequence of positive random variables $X_1, X_2, ....$ with values in $N=\left\{0,1,2,...\right\}$ and $\lim_{i\rightarrow\infty}E[X_i]=0$, it holds that $\lim_{i\rightarrow\infty}P[X_i=0]=1$.

Intuitively, I understand this concept due to the law of large numbers, since as $i$ approaches infinity the expected value converges to the true mean 0, and the probability that $X_i$ equals the true mean converges to 1.

However, I am stumped as to how to use Markov's Inequality, $P(X\geq c)=E(X)/c$, to prove this. Any help is appreciated.