Question: 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

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).

(d) Explain why P(r ≥ m) = 1 – P (0) – P (1) – - - - – P(m – 1) for 1 ≤ m ≤ n?

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