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...

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.