1. ## E(1/sn) and var(1/sn)

Hi
i have a question, when we have continuous variables, how we can calculate var (1/sn)
can we always change summation and integral?

for example x1,...,xn have G(a,b) distribution funcation... how we can calculate var (1/sn)?

we know E(xi)=ab , var(xi)= ab^2

Best wishes
zayrsil

2. ## Re: E(1/sn) and var(1/sn)

If you can find a distribution function for sn, you can transform it into a distribution function for 1/sn (there is a nice formula for that, but I do not know its name). Using this, you can calculate Var(1/sn).
If the original probability distribution function is $P_f(x)$ and you want to find the distribution of g(x), it is something like $P_g(y)=\frac{P_f(g^{-1}(y))}{dg/dx}$ (check this), assuming g is invertible and differentiable.

Thanks MFB