Broad and narrow distributions

\includegraphics [width = 0.5\textwidth] {{/Home/alastair/teaching/probstats}/source/figures/hatom.eps}

You have seen this PDF before! It describes the radial separation of an electron and proton in a hydrogen atom. It provides an example of a `broad' PDF: the mean and the standard deviation of this PDF are comparable. You will find it explored in HQ3 .


\includegraphics [width = 0.6\textwidth] {{/Home/alastair/teaching/probstats}/source/figures/narrowexample.eps}

This example doesn't look very physical...but, in fact, it describes a vast class of physically important problems, in which the standard deviation is so tiny compared to the mean that the PDF is just a spike (or, in more formal mathematical language, a $\delta$-function).

We will discuss the circumstances in which this happens in S5 .

When --eventually --you come to study Thermodynamics you might care to consider that its success rests entirely on this phenomenon.