# Central limit theorem

• January 3rd 2010, 05:20 PM
silk23
Central limit theorem

Hi i need some help with the question below, struggling to know how to apply the central limit theorem,

The Xi are a sequence of independent identical random variable with the given distrabution below

thanks for any help
• January 3rd 2010, 08:41 PM
matheagle
First obtain the CDF of the max of your sample.

Let $Y_n=max\{X_1,\ldots X_n\}$

$F_{Y_n} =\biggl(F_{X_i}(x)\biggr)^n=\biggl({x\over\theta}\ biggr)^n$

So $P(n(\theta-Y_n)\le x) =1-P\biggl(Y_n\le \theta -{x\over n}\biggr)=1-\biggl(1-{x\over\theta n}\biggr)^n$

$\to 1-e^{-x/\theta}$

and why do you think the CLT is involved here?
Not all convergences in distribution are to a normal.
Plus we're not observing a sum here either.
• January 4th 2010, 05:15 AM
silk23
question before involved CLT, was being a fool

thanks for you help