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 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)).
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 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)).
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.3: Binomial Probability
Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...
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