Let ${X}_{n}$ be a geometric random variable with parameter $p=\lambda /n$. Compute $P({X}_{n}/n>x)$

$x>0$ and show that as n approaches infinity this probability converges to $P(Y>x)$, where Y is an exponential random variable with parameter $\lambda $. This shows that ${X}_{n}/n$ is approximately an exponential random variable.

$x>0$ and show that as n approaches infinity this probability converges to $P(Y>x)$, where Y is an exponential random variable with parameter $\lambda $. This shows that ${X}_{n}/n$ is approximately an exponential random variable.