Let X₁, . . . , Xn be a random sample from an exponential distribution with density function f(x|?) = ?exp[??x], where ? > 0.

a. what is the critical region of a ? test of H₀: ? equals to ?₀ VSH₁: ? does not equal to ?₀ is of the form

Estimate c for a test of size 0.05 when n=10 and ?₀=1 by using the central limit theorem.

b. Show the critical region of a generalised likelihood test for this problem has the same form and use Wilks' Theorem to estimate c.

please explain it in detail... thank you