# Math Help - expectation of 1-(1/xbar)

1. ## expectation of 1-(1/xbar)

1-(1/xbar) for lambda is biased. Thank-you.

If we have a random sample X1,....,.Xn from a pareto distribution with pdf

f(x;lambda)= (1/lambda)x^(-(1+1/lambda))

then what is E[1-(1/xbar)]?

2. I guess the support is $(1,\infty)$

I don't think there is a nice MGf here.
We need the density of the sum of paretos.
dividing that by n and the rest would be easy.
But we would need to figure out the density of a sum of n iid paretos.

If you try to obtain the MGF and ley Y=X-1 you can almost make it a gamma density