Let x be a random variable such that PXk=k for k {1, 2, 3, k} we draw n independent samples from X and form a random vector C = [C1,C2,,CK]T where Ck is the number of times that kth values appears,

i. Derive an expression for the probability of C in terms of 1,2,...,k

ii. Derive the ML estimator for the parameters i for i {1,2,3,,k} (Note: i=1Ki=1 )

iii. Is the estimator derived in (i) unbiased? what is its variance?