# Thread: hypothesis testing_best test

1. ## hypothesis testing_best test

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

Consider the simple hypothesis
Ho: $theta$ = $theta$' = 2 versus
Ha: $theta$ = $theta$" = 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.