Problem 1H Let X have the distribution given below. Here 0

Problem IH Let X have the distribution given below. Here 0 < 0 < 1/3. value 3 probability 0 20 1 30 Let Xl,X2,... , Xn be i.i.d., drawn from the distribution above, independent of X. Let X(n) = (Xl + X2 + + Xn)/n. In each of parts (a), (b), and (c), classify the given quantity as a random variable or a real number. If you say "both" , explain your answer. If possible, compute the value of the quantity. You can leave your answer in terms of 0 if necessary. Problem 11 Continuing Problem 8 Say whether each of the following statements is true or false. Justify your answer. a) X(n) = E(X) for all n. E(X) for all n. c) If n is large, X(n) is likely to be equal to E(X) d) If n is large, X(n) is likely to be close to E(X) Problem IJ Continuing Problems 8 and 9 Use the results of Problems 8 and 9 to come up with anbased on X(n). Is your estimate a random variable or a real number? Show that your estimate has at least one desirable property.