here's my question

3. Let X be a geometric random variable with parameter 0, where 0 is an unknown parameter. Let X1, ..., Xn be a random sample of X. a . Suppose that the parameter space is $ = {1/4, 1/2,3/4}, that the size of our random sample is n = 4, and that we observe X1 = 5, X2 = 4, X3 = 1, X4 = 3. Find the maximum likelihood estimate for 0. b . In homework, it was shown that Y = _ Xi is a sufficient statistic for 0. Show that Y has the key property of a sufficient statistic by showing that the probability n P(X1 = x1, . .., Xn = an| Y = y), where X1, . . ., In are positive integers and y = i=1 does not depend on the unknown 0