Consider an experiment in which two dice are thrown at the same time, and the outcome is an ordered pair of the numbers that show up on each die's top face after coming to rest. Assume that we are careful to specify and distinguish a "?rst" die (black die with white spots) from the "second" (white die with black spots) (1) Obtain the sample space of all possible outcomes. (2) De?ne a random variable X as the sum of numbers that show up on the two dice; obtain the new space V arising as a result of the application of this random variable.