1. Let X be a random variable representing the minimum of the two numbers of dots that are facing up af ter a pair of fair dice is rolled. Define the appropriate prob ability density for X. What is the probability space for the experiment of rolling the fair dice and observing the minimum of the two numbers of dots?
2. A package of a half-dozen light bulbs contains two defective bulbs. Two bulbs are randomly selected from the package and are to be used in the same light fix ture. Let the random variable X represent the number of light bulbs selected that function properly (i.e., that are not defective). Define the appropriate probability density function for X. What is the probability space for the experiment?