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**statmajor** 1. Let Xn denote the mean of a random sample of size n from a distribution that is $\displaystyle N(\mu, \sigma ^2)$. 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 $\displaystyle f(x) = e^{-(x - \theta)} \ \ \theta < x $. Let $\displaystyle Z_n = n(Y_1 - \theta)$. Find the distribution of Zn.

1.

So to find the limiting distribution, I need to take the limit of the PDF as n approaches infinity.

$\displaystyle X_n = \frac{X_1 + X_2 + ... + X_n}{n} = \frac{nX_n}{n} = X_n $

Kinda stuck here.

Any help would be appreciated.