I have a 5-part assignment. I wrote the first 2 chapters myself. A friend of yours wrote the 3rd part here and it turned out to be plagiarized. Chapter 3 will be edited, and once chapter 3 is completed. 4 and 5 will be written. But this assignment is a continuation of each other.
Assume a r.v. >0 in a probability space ( , , ) with (*) and survivalfunction / ( )(*).Let (*) be the tail quantile function of , show that for
Assume a r.v. >0 in a probability space ( , , ) with (*) and survivalfunction / ( )(*).Let (*) be the tail quantile function of , show that for any pin(0,1), wehave / ( )( (1 ))≤ .Show that the first two definitions of the SOC (secondary order condition),i.e. (**1) and (**2) are equivalent.Given →0, prove the following with given fact that . (1(/