Understanding Basic Statistics 6th Edition by Charles Henry Brase,Corrinne Pellillo Brase

Exercise 18

Critical Thinking Let r be a binomial random variable representing the number of successes out of n trials.
(a) Explain why the sample space for r consists of the set {0. 1, 2,…, n} and why the sum of the probabilities of all the entries in the entire sample space must be 1.
(b) Explain why P ( r 1) = 1 P (0).
(c) Explain why P ( r 2) = 1 P (0) - P (1).
(d) Explain why P ( r m ) = 1 - P (0) - P (1) … P ( m - 1) for 1 m n.