A monkey randomly presses n keys of a computer. For simplicity, assume each key press is one of the 26 letters of the English alphabet. Each key press is independent of all previous presses, and equally likely to be one of the 26 letters. Thus, there are 26" possible combinations of letters, all equally likely. a) Compute the expected number of occurrences of hello. Justify your work. b) Let X be the sum of the number of occurrences of "hello and goodbye. For example, if there are 2 occurrences of hello and 1 occurrence of goodbye then X = 3. Compute E [X]. A monkey randomly presses n keys of a computer. For simplicity, assume each key press is one of the 26 letters of the English alphabet. Each key press is independent of all previous presses, and equally likely to be one of the 26 letters. Thus, there are 26" possible combinations of letters, all equally likely. a) Compute the expected number of occurrences of hello. Justify your work. b) Let X be the sum of the number of occurrences of "hello and goodbye. For example, if there are 2 occurrences of hello and 1 occurrence of goodbye then X = 3. Compute E [X]