This is the question

2. [3|] points} Let X1, . . . ,X be i.i.d. Bernoulli{p} random variables. Specically X1- is a discrete random variable with P.M.F.: P[X=1}=p;P[X;=G}=1p. Consider testing the hypotheses {a} [It] points} Show that the GLHT has the form r111 _ my? :- c, where f = % ELI X1- is the sample mean and c is a constant that depends on the size of the test :1. [b] {1U points} Use your answer to part {a} and the asymptotic distribution of the GLRT to derive the value for c (in the form written} when o: = {1.135. If n = 1m and T = [1.5, would you accept or reject the null hypothesis? Explain your answer. {(3} {1D points} Show that the test in part [a] is equivalent to the test If %| 1::- c' for a constant c" that depends on o:. Use the central limit theorem {normal approximation] to derive c'r for CE = llti. If n = 100 and f = [1.5, would you accept or reject the null hypothesis? Explain your