Let the random variable X have the pdff(x;$\displaystyle theta$) = (1/$\displaystyle theta$)exp{-x/$\displaystyle theta$), 0 < x < $\displaystyle infinity$, zero elsewhere.

Consider the simple hypothesis

Ho: $\displaystyle theta$ = $\displaystyle theta$' = 2 versus

Ha: $\displaystyle theta$ = $\displaystyle theta$" = 4.

Let X1, X2 denote a random sample of size 2 from this distribution. Show that the best test of Ho against Ha may be carried out by use of the statistic X1 + X2.