Let {Xi} n i=1 be a random sample from a population with E [X] = 2, E [X2 ] = 6, E [X3 ] = 1 and E [X4 ] = 37. (a) Let X¯ n = 1 n Xn i=1 Xi . Compute the probability limit of 3 X¯ n + 1 as n → [infinity]. Please state all the results you have used to obtain your answer, explaining the reasons of why you can use them (generic answers are not accepted).
(b) Let g¯n (X) = 1 n Xn i=1 X 3 i . Compute the probability limit of 2¯gn (X) as n → [infinity]. Please state all the results you have used, explaining the reasons of why you can use them (generic answers are not accepted).
(c) What distribution does √ n 5X¯ n − 10 2 converge to? Please state all the results you have used, and explain the reasons of why you can use them (generic answers are not accepted). The mean and variance of the limit distribution should be presented as numbers, and not in generic terms.

What is the area of a pizza with a radius of 40 cm leave the answer in terms of π to find your exact answer 40π cm² 1600π cm² 800π cm² 80π cm² π=pi

Tim open up a new saving account with a $50 deposit and plant to deposit $20 per week into the same account. write an expression to represent the total amount in his savings account.

Write the contrapositive of the conditional statement. determine whether the contrapositive is true or false. if it is false, find a counterexample. a converse statement is formed by exchanging the hypothesis and conclusion of the conditional. a) a non-converse statement is not formed by exchanging the hypothesis and conclusion of the conditional. true b) a statement not formed by exchanging the hypothesis and conclusion of the conditional is a converse statement. false; an inverse statement is not formed by exchanging the hypothesis and conclusion of the conditional. c) a non-converse statement is formed by exchanging the hypothesis and conclusion of the conditional. false; an inverse statement is formed by negating both the hypothesis and conclusion of the conditional. d) a statement not formed by exchanging the hypothesis and conclusion of the conditional is not a converse statement. true