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1. The random variable X has a binomial distribution with E(X)=7.5 and Var(X)=5.25. Find n and p for this distribution. 2. Suppose X is a binomial random variable with n=10 and p=0.1. Feel free to use a computer to answer the following: a) P(X=0) b) P(X=2) c) P(X<2) d) P(X>8) e) E(X) f) Var(X) 3. A survey on British Social Attitudes asked respondents if they had ever boycotted goods for ethical reasons (Statesman, January 28, 2008). The survey found that 23% of the respondents have boycotted goods for ethical reasons. Using the binomial distribution (and a computer if you want), answer the following questions. a) In a sample of six British citizens, what is the probability that two have ever boycotted goods for ethical reasons? b) In a sample of six British citizens, what is the probability that at least two respondents have boycotted goods for ethical reasons? c) In a sample of ten British citizens, what is the probability that none have boycotted goods for ethical reasons? d) In a sample of ten British citizens, what is the expected number of people that have boycotted goods for ethical reasons? 4. The joint probability mass function of random variables X and Y is given by Are X and Y independent? Justify your answer 5. A large insurance agency services a number of customers who have purchased both a homeowner's policy and an automobile policy from the agency. For each type of policy, a deductible amount must be specified. For an automobile policy, the choices are $100 and $250, whereas for a homeowner's policy, the choices are 0, $100, and $200. Suppose an individual with both types of policy is selected at random from the agency's files. Let X = the deductible amount on the auto policy, and Y = the deductible amount on the homeowner's policy. Suppose the following table represents the joint distribution of X and Y: a) What are the mean and standard deviation of X? b) What are the mean and standard deviation of Y? c) What is the covariance between X and Y? d) What is the correlation between X and Y? e) Are X and Y independent? Justify your answer. 6. Suppose a game involves dropping 3 coins on the tableā€”a nickel, a dime, and a quarter. Each coin that lands "heads up" you are allowed to keep, so that the possible reward R ranges from 0 to 40c. We found the expected value of R. For this problem, now find Var(R).

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