Past exam of the options I course of the University of Oxford / 2013 / M / 2 / b

Put $Y_n=n(1-M_n)\ge 0$. For fixed $x\ge 0$ and sufficiently large $n>x$,For $x<0$ its distribution function is zero. The limiting distribution function is therefore $F(x)=0$ for $x<0$, $F(x)=1-e^{-x}$ for $x\ge 0$, the exponential distribution of rate one. Since this distribution function is continuous everywhere,