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
First obtain the CDF of the max of your sample.
Let $\displaystyle Y_n=max\{X_1,\ldots X_n\}$
$\displaystyle F_{Y_n} =\biggl(F_{X_i}(x)\biggr)^n=\biggl({x\over\theta}\ biggr)^n $
So $\displaystyle 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 $
$\displaystyle \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.