Past exam of the options II course of the University of Oxford / 2011 / M / M4 / d

For $x\ge 0$, the geometric distribution tail givesFor $x<0$, $P(T_k\le x)=0$. The limiting cumulative distribution function is therefore $0$ for negative $x$ and $1-e^{-x}$ for nonnegative $x$, and it is continuous everywhere. This proveswith rate parameter $1$ and mean $1$.