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Problem 9 (5 points). Assuming that X ~ Uni(0,l), a uniform random variable in range between 0 and 1, nd mean and variance of random variable Y = 3X + 2. 3Eyj Problem 10 (5 points). The following problem is related to Bayes Theorem that is stated as P(A|B) = PfBiA)P(A)/P{B), where A and B are random variables. Let us assume A is a binary random variable stating whether a woman has breast cancer and B is a binary random variable stating whether a woman tested positive on a mammogram. Let us a assume the following background knowledge: 0.1% of women have breast cancer; 90% of women who have breast cancer test positive on mammograms; 8% of healthy women test positive on mammograms. What is the probability that a woman has cancer if she has a positive mammogram result? What is the probability that a woman has cancer if she has a negative mammogram result