The Fisher informationI(p;f1,f2) for estimating the proportionpin a mixture λ(x) =pf1(x) +(1 −p)f2(x) of two densities is investigated. A general power series expansion is obtained, which is then explored in detail for the case of two exponential densities, and for the case of two normal densities with equal scale. Simple approximations are obtained, for example