Let X1, ..., Xn be a random sample from an exponential distribution, Xi ~ EXP(theta).
a) Derive the generalized likelihood ratio test of Ho: theta = theta(not) against Ha: theta not equal to theta(not). Determine an approximate critical value for size alpha using the large-sample chi-square approximation.
b) Derive the generalized likelihood ratio test of Ho: theta = theta(not) against Ha: theta > theta(not).