In Alpha College, students are required to join at least one school club to get extra-curriculum activities' marks. Suppose the following table represents the probability distribution function of the...

Extracted text: In Alpha College, students are required to join at least one school club to get extra-curriculum activities' marks. Suppose the following table represents the probability distribution function of the number of clubs (X) a student join: 1 2 3 4 P(X = x) 0.1 2k k + 0.1 k (a) Find the value of k. (b) What is the probability that a student joins at most two clubs? (c) Find E(X), Var(X) and o(X). (d) Suppose the membership fee is $100 per club, with the first enrolled club is free of charge. Let Y be the total membership fee a student pay. Compute E(Y) and o(Y). (e) What percentage of students are paying not less than $200 for the total membership fee? (f) Write a simple paragraph (about 30 -50 words) to summarize the total membership fee a student paying for joining school club(s) (based on the results in parts (d) and (e)).