# Distribution function problem - (maybe) difficult

• Apr 1st 2009, 12:56 AM
Bjorn
Distribution function problem - (maybe) difficult
I’ll try this again, since I didn’t get a solution last time

• Apr 1st 2009, 09:32 AM
Laurent
Quote:

Originally Posted by Bjorn
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 $n\to\infty$.
$P(Z_n\leq t)=P(n(\theta-S_n)\leq t)=P(S_n\geq\theta-\frac{t}{n})=1-P(S_n< \theta-\frac{t}{n})=\cdots$
I get an exponential $\theta$.