Consider estimating the binomial parameter k as in Example 7.2.9. a. Prove the assertion that the integer

Question:

Consider estimating the binomial parameter k as in Example 7.2.9.
a. Prove the assertion that the integer that satisfies the inequalities and is the MLE is the largest integer less than or equal to 1/.
b. Let p = 1/2, n = 4, and X1 = 0, X2 = 20, X3 = 1, and X4 = 19. What is ?