Question 24: Suppose a remote town contains 1000 men, consisting of 100 Atheist Blue-eyed Canadians, 50 Atheist Canadians with green eyes, 100 Atheist Blue-eyed Russians, 150 Atheist green-eyed Russians, 150 Christian Blue-eyed Russians, 50 Muslim Blue-eyed Canadians, and 175 Christian green-eyed Canadians. Draw a Venn diagram indicating the probabilities of someone in the town being Atheist (A), Blue-eyed (B), Canadian (C), or any combination of the above. If you pick a Canadian from your sample at random, what is the probability that he is both Atheist and Blue-Eyed? Is this the same as the probability that a Blue-eyed Atheist in your sample is Canadian? Explain, using Boolean algebra. The mayor of the town asserts that Blue-eyed (B) people are no more likely to be Atheists (A) than anyone else. Is this true? Can you conclude anything about the statistical independence of atheism and blue eye color? Are A, B, and C mutually independent traits? Define a random variable that you could create by drawing a person at random from the people in the town and noting his nationality, religion, and eye color. What is the sample space, probability (density) function, mean, variance, skewness coefficient, and kurtosis coefficient of your random variable?