Can't manipulate RV like that when it comes to distributions. Best way is to go through the moment generating function. You should expect to get another normal distribution .
1. Let Xn denote the mean of a random sample of size n from a distribution that is . Find the Limiting distribution of Xn.
2. Let Y1 denote the first order statistic of a random sample of size n from a distribution that has the PDF . Let . Find the distribution of Zn.
So to find the limiting distribution, I need to take the limit of the PDF as n approaches infinity.
Kinda stuck here.
Any help would be appreciated.
Post #2 told you the distribution. Your job is to understand why this is the distribution. Your job is also to review how to get the moment generating function of a sum of independent random variables.
Then you have to take the limit of the distribution as n --> +oo. The result is unsurprising (Google Dirac delta function).
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