Averages in involving multiple continuous variables Suppose you want to compute the average of something like height (h) $\times$ weight (w), for a population of chipmunks. This involves two separate variables. You might have the distribution $P(h,w)$ which is a probability density. $P(h,w) dh dw$ is the probability of finding a chipmunk of height between $h$ and $h+dh$, and weight between $w$ and $w+dw$. In this case we can then define the average as $$\langle h w\rangle = \int\int h w P(h,w) dh dw$$ (1.32) This is for a continuous distribution For a discrete one, you'd replace the integrals by summation, as we saw in above in the one dimensional case.