MLE Example 1. Suppose X1, . . ., Xn are i.i.d. Bernoulli(p). Find the MLE of p. 2. Hint: X; has the distribution f(x;; p) = p*i(1 - p)1-xi Answer: 1. maxpelo,1] Li_1 log(f(Xi; p)) = maxpelo,1] y log p + (n - y) log(1 - p) where y = _i-1xi 2. First derivative of log likelihood is - n-y P (1-p) 3. Second derivative is - ny ( 1-p ) 2 4. Differentiating and setting to 0 yields Pm/ = EM-1 Xi n