I have a 6-chapter assignment. I wrote the first 2 chapters myself. Currently, 3-4-5-6 chapters will be written, but according to dates. Chapter 3 will be written first.but all the chapters are 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(/