2. Let y1, ..., yn be realisations of n iid random variables with probability mass function f (y; 0) = ex (1 - 0 ) 1 - 09 y = 0, 1, 2, ... , 7, 8 for some unknown parameter 0 E (0, 1). Hint. For this distribution, 909 E(Y) = 8109 1 - 0 1 - 09 and var(Y) = (1 - 0)2 (1 - 09)2.a) The log likelihood function for 0 is given by O a. f(0) = log(0) Zi=1 yi + nlog(1 - 0) - nlog(1 - 09) O b. e(0) = log(0) _1=1 yi - nlog(1 - 0) + nlog(1 - 09) O c. e(0) = log(0) _1=1 yi + nlog(1 - 0) + n[1 -9log(0)] O d. e(0) = log(0)ny - nlog(1 - 0) + nlog(1 - 09)