2. Let y1, Yn be realisations of n iid random variables with probability mass function 03 (1 - 0) f(y; 0) = 1-09 y = 0, 1, 2, ..., 7,8 for some unknown parameter 0 (0, 1). Hint. For this distribution, 909 E(Y) = 8109 and var(Y): = 1 - 0 1 - 09 (1 - 0)2 (109)2 a) The log likelihood function for 0 is given by a. (0) = log(0) 1 y; + n log(1 0) n log(1 0) - - b. c. d. =1 (0) = log(0) -1 y; n log(1 0) + n log(1 0) i=1 - _ - (0) = log(0) 1 y; + n log(1 0) + n[1 9 log(0)] (0) = log(0)ny n log(1 0) + n log(1 0) - -