18. Let X1,...,Xn be independent random variables having a common distribution function that is specified up to an unknown parameter θ . Let T = T (X)

be a function of the data X = (X1,...,Xn). If the conditional distribution of X1,...,Xn given T (X) does not depend on θ then T (X) is said to be a sufficient statistic for θ . In the following cases, show that T (X) = n i=1Xi is a sufficient statistic for θ .