Normalise a density

A valid density satisfies f(x)≥0 and total integral 1. P(a<X<b)=∫ from a to b f(x)dx, restricting to the support. A density can exceed 1 on a short interval; its area, rather than height, is a probability. If f(x)=kg(x), integrate g over the support, then set k equal to the reciprocal of that integral.