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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?

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