DESCRIPTION Please keep in mind the OMSI rules. Save your files often. Submit each answer individually and make sure you receive the notification of successful submission. Don't wait till the last moment to submit all answers, as there might be network traffic in the last 5 minutes causing unexpected delay and failure. Remember that clicking CopyQtoA will copy the entire question box to the answer box. In questions involving code which will PARTIALLY be given to you in the question specs, you may need to add new lines. There may not be information given as to where the lines should be inserted. MAKE SURE TO RUN THE R CODE ANSWER IN PROBLEMS THAT INVOLVE R CODE! QUESTION (Text answer - 25 pts) Let X be a random variable that denotes the values taken by a fair dice. We can say that the set {1, 2, 3, 4, 5, 6} is ______________ of X. QUESTION (Text answer - 25 pts) Say we have a random sample X_i, i = 1,2,...,n, with population cdf F_X(t). X is a continuous random variable. Let G denote the empirical cdf. Which is/are true? (i) G(t) is a nondecreasing function. (ii) G(t) is a nonincreasing function. (iii) G(t) has n points of discontinuity. (iv) G(t) is continuous. (v) The number of points of discontinuity of G could be nonzero but a number other than n. (vi) G(t) is a random variable. (vii) None of the above is true. QUESTION (Text answer - 25 pts) The reason that the early pioneers of statistics defined sample variance in the "divide by n-1" way was that dividing by n yields a ______________ estimator of the population variance. (Fill in the blank with an official term from our course.) QUESTION -ext .R -run 'Rscript ./omsi_answer4.R' (R Code answer - 25 pts) Say we have a random sample X_i, i = 1,2,...,n, with population cdf F_X(t). Let G denote the empirical cdf. Suppose (unknown to the one analyzing the data), X has a uniform distribution on [40,60]. Find Var[G(48.8)]. print()