Distribution function problem - (maybe) difficult

**Bjorn** · April 1st 2009, 12:56 AM

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

Please see the attached

**Laurent** · April 1st 2009, 09:32 AM

Originally Posted by Bjorn

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

Please see the attached

Now you should compute the distribution function of $Z_n$ and prove that it converges to some limit when $n\to\infty$ .

$P(Z_n\leq t)=P(n(\theta-S_n)\leq t)=P(S_n\geq\theta-\frac{t}{n})=1-P(S_n< \theta-\frac{t}{n})=\cdots$

**matheagle** · April 1st 2009, 10:44 PM

I get an exponential $\theta$ .

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