TQ5 Molecular speeds: expectation values

Write down the definition of the expectation value $\langle g(x) \rangle$ of some function g of a random variable X. Explain what it means.

Write down the definitions of the mean and the standard deviation of X. Explain what they mean.

The PDF for the molecular speeds in a gas is given by the Maxwell distribution:

f(v) = Av2 e-Bv2

Here A and B are `constants' in the sense that they do not depend upon v.
1.
Sketch how the PDF varies with v.
2.
Write down an equation for A (in terms of B).
3.
Estimate (in terms of the constants A and B) the mean and the standard deviation of the speed.