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Question: Suppose that six of the 15 school buses in a particular school district have developed a slight defect since their last inspection (the steering wheel shakes when braking). Five buses are to be selected for thorough inspection. Let X denote the number of buses among the five that are inspected that have the defect.

(a) The random variable X is (choose one)

(i) binomial

(ii) hypergeometric

(iii) negative binomial

(iv) Poisson.

(b) Give the sample space and formula for the PMF of X.

(c) Use R commands to find P(2 ≤ X ≤ 4).

(d) Give the expected value and variance of X.

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