What does the marginal density of a distribution actually represent?

Question

What does this represent intuitively?

http://en.wikipedia.org/wiki/Marginal_density

Thanks!

I'm not sure I'm getting you. Could you please elaborate on what the fringe value is?

Thanks modulo_function. Would I be right to say that this is just the probability of any single variable regardless of the other variable? (An "average probability"?)

Answer 1

Let's say you have a 2 by 2 table of gender (m/f) rows and smoker (y/n) columns. Adding across rows or columns and normalizing gives probabilites separately. The name comes from the fact that you'd write these sums in the margins of your table. This description is for descrete distributions. Of course you'd integrate for continuous densities. Under certain conditions, i.e., independence, to find the joint probability that someone in you sample is m and a smoker, you'd multiply the marginals.

Answer 2

The fringe value of the data.