Listing of abstract file abs.tex

\begin{abstract}

We give simple proofs of two well-known related results: (1) the
probability density function of Student's t distribution with v
degrees of freedom converges to the standard normal density, and (2)
the sample standard deviation $S$ of a random sample from a normal
distribution with variance $\sigma^2$ is asymptotically unbiased for
$\sigma$. Our proof does not use Stirling's approximation to the gamma
function, but relies on the recursive property of the gamma function,
elementary properties of convergent sequences and the fact that
$E(S) \leq \sigma$.

\end{abstract}
KEY WORDS: Gamma function, Standard deviation, Asymptotically unbiased,
Chisquare distribution