Question 2: Discrete Random Variables (15 points) 1. (5pts) When do you use a Bionomial random variable to model a statistical experiment? When do you rather use a Hypergeometric random variable? Explain briey. 2. (5pts) Consider an aggregate of 12 lithium batteries. Suppose that the probability of an individual lithium battery being defective independently of all other batteries is 30%. Let X be the number of defective batteries in an aggregate. What is the probability P(X > 9)? 3. (5pts) Suppose that 24 lithium batteries were used to construct 2 aggregates of 12 batteries each. If there were exactly 5 defective batteries among the 24 batteries, what is the probability that all 5 defective batteries are used in the same aggregate