Suppose the discrete random variable of interest, a, is the number of rolls that result in a composite number when rolling a die three times (LI and E are the possible composite numbers when rolling a die}. Use this scenario to answer questions 315. 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 probabity for each of the outcomes in the tree diagram. 11) Create the probability distribution for X {the numb er 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 satised? 13] Calculate the mean (expected value) for X. 14) Calculate the variance for x. 15} Calculate the standard deviation for x. We will consider a simple lottery wager, the straight from a pick. 3 game. You pay $0.50 and choose a threedigit number. The state chooses a threedigit winning number at random and pays $250 if your number is chosen. Because there are 1000 three-digit numbers, you have probability 1t1000 = 0.001 of winning. Below is the discrete probability distribution for the winnings. Use this information to answer questions 10-18. 1ft} Calculate the mean of x. 1?) Calculate the variance of X. 10] Calculate the standard deviation of x