Suppose that X1, , Xn form a random sample from a distribution for which the p d f is f (x ), where the value of the parameter belongs to a given parameter space Suppose that T r(X1, , Xn) and T ' r ' (X1, , Xn) are two statistics such that T ' is a one to one function of T that is, the value of T ...

The statistic T will be a sufficient statistic for if and only if f n x can be fac ...

Suppose that X1, . . . , Xn form a random sample from a distribution for which

Question:

Suppose that X1, . . . , Xn form a random sample from a for which the p.d.f. is f (x|θ), where the value of the parameter θ belongs to a given parameter space Ω. Suppose that T = r(X1, . . . , Xn) and T' = r' (X1, . . . , Xn) are two statistics such that T' is a one-to-one function of T; that is, the value of T' can be determined from the value of T without knowing the values of X1, . . . , Xn, and the value of T can be determined from the value of T' without knowing the values of X1, . . . , Xn. Show that T' is a sufficient statistic for θ if and only if T is a sufficient statistic for θ.
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...