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.

This is so hard and it’s for a test

Look at this pattern ; 1,4,9, number 10000 belongs in this pattern . what’s the place of this number?

Design an er diagram for keeping track of information about votes taken in the u.s. house of representatives during the current two-year congressional session. the database needs to keep track of each u.s. state's name (e.g., texas', new york', california') and include the region of the state (whose domain is {northeast', midwest', southeast', southwest', west'}). each congress person in the house of representatives is described by his or her name, plus the district represented, the start date when the congressperson was first elected, and the political party to which he or she belongs (whose domain is {republican', democrat', 'independent', other'}). the database keeps track of each bill (i.e., proposed law), including the bill name, the date of vote on the bill, whether the bill passed or failed (whose domain is {yes', no'}), and the sponsor (the congressperson(s) who sponsored - that is, proposed - the bill). the database also keeps track of how each congressperson voted on each bill (domain of vote attribute is {yes', no', abstain', absent'}). additional information: