Cody Buehler

My name is Cody Buehler, and I grew up here in St. Joseph. I'm a Mathematics major, and plan to use my degree to become an actuarial scientist. This is my last semester here at MWSU, and it couldn't have come any sooner. I don't particularly have a "favorite" math theorem, but one I find quite useful is the Central Limit Theorem:

Let $Y_1, Y_2,...,Y_n$ be independent and identically distributed random variables with $E(Y_i)=\mu$ and $V(Y_i)=\sigma ^2 < \infty$. Define

(1)

\begin{align} U_n= \frac{\sum_{i=i}^{n} Y_i - n\mu}{\sigma \sqrt{n}} = \frac{\bar{Y} - \mu}{\sigma \: / \sqrt{n}} \;\;\; \text{where} \; \bar{Y} = \frac{1}{n} \sum_{i=1}^{n} Y_i . \end{align}

Then the distribution function of $U_n$ converges to the standard normal distribution function as $n \to \infty$. That is,

(2)

\begin{align} \lim_{n \to \infty} P(U_n \leq u) = \int_{- \infty}^u \frac{1}{\sqrt{2\pi}}e^{\frac{-t^2}{2}} \! \: dt \;\;\; \text{for all} \: u. \end{align}

This is very useful since it allows you to take raw data and relate it to a distribution in order to calculate various probabilities.

Lastly, here is a picture of me and my girlfriend enjoying a few drinks: