Problem 5. Let X have the distribution given below, in which 0

Problem 5. Let X have the distribution given below, in which 0 < 0 < 1/6: value 4 12 e3 probability 20 0 30 1 60 , Xn be i.i.d observations drawn from the distribution above, each Let X], {1, 2, 3, 4}. Express the likelihood function of the type Xi = where L(O) and the log-likelihood 1(0) in terms of number of samples equal to 1, nl = number of samples equal to 2, n2 = number of samples equal to 3, n3 number of samples equal to 4. Note that n + + n3 + n4. Find OMLE in terms of the above nt's.