Suppose the discrete random variable of interest, x, is the number of rolls that result in a composite number when rolling a die three times (4 and 6 are the possible composite numbers when rolling a die). Use this scenario to answer questions 8-15. 8) Create a tree diagram for the three rolls of the die letting C= {composite number rolled} and N = {composite number not rolled). 9) How many outcomes are there in the tree diagram? 10) Calculate the probability for each of the outcomes in the tree diagram. 11) Create the probability distribution for x (the number of times a composite number is rolled when rolling a die three times). 12) To verify that this is a valid discrete probability distribution, what properties must be satisfied? 13) Calculate the mean (expected value) for x. 14) Calculate the variance for x. 15) Calculate the standard deviation forx

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