Let X1, , Xn be iid with geometric distribution P(X x) (1 )x 1, x 1, 2, , 0 1 Show that Xi is sufficient for , and find the family of distributions of Xi Is the family complete ...

The population pmf is f x 1 x1 1 e log ...

Let X1,..., Xn be iid with geometric distribution P(X = x) = (1 - )x-1, x =

Question:

Let X1,..., Xn be iid with geometric = x) = θ(1 - θ)x-1, x = 1, 2,..., 0 < θ < 1.
Show that ∑Xi is sufficient for θ, and find the family of distributions of ∑Xi. Is the family complete?
Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...