For the following three questions, consider the following STATA program: /* beginning of the program */ clear cap postclose tempid postfile tempid beta test_outcome /// using mydata.dta,replace forvalues i = 1(1)10000 { drop_all quietly set obs 10000 gen x = rnormal() gen e = rnormal() gen y = x^3 + e quietly reg y x, r scalar beta = _b[x] qui test x = 3 sca test_outcome = (r(p)>0.1) post tempid (beta) (test_outcome) } postclose tempid use mydata.dta, clear sum /* end of the program */ The "sum" command will give us the mean and standard derivation of beta and test_outcome. It is known that E (X4) = 3 for a standard normal X.

ONLY IF STATEMENTS ALLOWED!!!! NO RANGE FUNCTION, NO SETS, NO LISTS, NO LOOPS, ETC Angela loves reading books. She recently started reading an AI generated series called “Harry Trotter”. Angela is collecting books from the series at her nearest bookstore. Since the series is AI generated, the publishers have produced an infinite collection of the books where each book is identified by a unique integer. The bookstore has exactly one copy of each book. Angela wants to buy the books in the range [l,r], where l ≤ r. As an example, the range [−3,3] means that Angela wants to buy the books  − 3,  − 2,  − 1, 0, 1, 2, and 3. Dan also loves the series (or maybe annoying Angela – who knows, really), and he manages to sneak into the bookstore very early to buy all of the books in the range [d,u], where d ≤ u. When Angela later visits, sadly she will not find those books there anymore. For example, if Angela tries to buy books [−2,3] and Dan has bought books [0,2], Angela would only receive books…