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3) Out of 5000 students at a university, 1000 get picked at random (with replacement). These students get asked if they know the name of the dean. Let p be the proportion of students among the 5000 which know the name of the dean. Out of the 1000 surveyed, 800 know the name of the dean. a) Estimate p. b) Give : 95% confidence interval for p. c) Assur e that the school would have 100000 students instead of 5000. Assume again that we pick 100) at random (from the 100000) and that 800 know the name of the dean. Give a 95%- confide ce interval for p. What do you notice? d) If we survey 100 times more people, how much smaller does the 95%-confidence interval get? Why? Let X1, X2, X3, . .. be i.i.d. variables taking values between +1 and too with probability density given by: f(x) = - d - 1 for every r 2 1 where A > 1 is an unknown parameter. For r