Question 3 Harry must speak Parseltongue (a language of snakes) to open the entrance to the Chamber of Secrets. All the words in Parseltongue have exactly seven characters formed from the characters {S, NA, KE} arranged in some order where the paired letters cannot be separated. For example, "SSSSSSS" and "NASSKESKES" are words in the language but "SANKESSKES" and "SNAKSESNANA" are not. (a) Find the numer of possible words in Parseltongue. (b) The password to open the Chamber of Secrets is one of the words in Parseltongue, which is randomly generated with the probabilities P(S) = 0.2, P(NA) = 0.3 and P(KE) = 0.5. Let X be the total number of characters Ss in the password, Y and Z be the total number of characters NAs and KEs in the password respectively. Find (i) the CDF for Z (ii) P[( X = 2) ~(Y = 2) n(Z =3)] (iii) P[(Y 2 3) (Z 23) ] (iv) P[(Z - X) > 4] (v) P[(Y