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) 512P(0).

(c) Explain why P(r $ 2) 512P(0) 2P(1).

(d) Explain why P(r $ m) 512P(0) 2 P(1) 2  2P(m 21)

P(r $ m) 512P(0) 2P(1) 2  2P(m 21) for 1 # m # n.

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