Imagine you have n iid random variables X, X2, Xn, with E[X] = and Var(X) =...

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Imagine you have n iid random variables X, X2, Xn, with E[X] = and Var(X) = for all i. Let X = 1 X be the sample average estimator. To get confidence intervals we used concentration inequalities. Using Chebyshev's inequality, we can say that Part (a) [10 MARKS] What is E[X]? P(|X-EX] > e) < 02 ne Part (b) [30 MARKS] Derive a 95% confidence interval for E[X], using the above inequality. Show your steps. (1) Imagine you have n iid random variables X, X2, Xn, with E[X] = and Var(X) = for all i. Let X = 1 X be the sample average estimator. To get confidence intervals we used concentration inequalities. Using Chebyshev's inequality, we can say that Part (a) [10 MARKS] What is E[X]? P(|X-EX] > e) < 02 ne Part (b) [30 MARKS] Derive a 95% confidence interval for E[X], using the above inequality. Show your steps. (1)

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