Let the random variable X have the pdf f(x; ) = (1/ )exp{-x/ ), 0 < x < , zero elsewhere.
Consider the simple hypothesis
Ho: = ' = 2 versus
Ha: = " = 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.