# Thread: Distribution function problem - (maybe) difficult

1. ## Distribution function problem - (maybe) difficult

I’ll try this again, since I didn’t get a solution last time

Now you should compute the distribution function of $Z_n$ and prove that it converges to some limit when $n\to\infty$.
$P(Z_n\leq t)=P(n(\theta-S_n)\leq t)=P(S_n\geq\theta-\frac{t}{n})=1-P(S_n< \theta-\frac{t}{n})=\cdots$
3. I get an exponential $\theta$.