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Problem 2. (25 points). You next begin to start attending concerts in person. Since you demanded riding the 801 bus as the rst activity after being fully vaccinated, your friends insist that they choose the concerts. Unfortunately your friends have highly questionable taste in music, and you are treated to a succession of shows by Ylvis, Pitbull, Robin Thicke, Silento, and others. So instead of listening to the music, you pay note to the size of the crowd and put your knowledge of probability and statistics to work. The crowd size is always between 0 and 1000 people. Let X denote the crowd size measured in thousands of people (so if 500 people show up, X = 0.5). You notice that the PDF of X is described by 633(1 7 x) if 0 S a: 5 1, and 0 otherwise. (a) (15) What is the mean and variance of X ? (b) (5) If tickets sell for $20 each, what is the mean and variance of the ticket sales for a concert? (c) (5) By the end of the year you have been subjected to 36 of these concerts. What is the probability that the mean attendance from these concerts is more than 530