STAT 3509 XXXXXXXXXXAssignment 2 XXXXXXXXXXWinter 2021 NOTE: Please submit the handwritten (detailed) work by e-mail XXXXXXXXXXas an attachment in pdf form) to your TA (only handwritten...

MLE, method of moments estimators


STAT 3509 Assignment 2 Winter 2021 NOTE: Please submit the handwritten (detailed) work by e-mail (as an attachment in pdf form) to your TA (only handwritten Solutions will be accepted!) Please name your pdf file as: Lastname.studentnumber.A2 Deadline: Thursday, January 28, 5:30 PM Let X1 , X2 , … , Xn represent a random sample from each of the distributions having the following pdfs : a) f (x ; ) =  x−, 0< x="">< 1,="">< ="" ="" ,="" zero="" elsewhere,="" b)="" f="" (x="" ;="" )="" −?/="" ,="">< x=""><     , zero elsewhere. in each case find the mle ̂ of . also, in each case, find method of moments estimators and show that they are consistent. hint: to show consistency, the first main result you need to use is wlln. then recall that for continuous functions convergence in probability is preserved (theorem 5.1.4). see also reviews that are posted on culearn. please note that you need only to show consistency of method of moments estimators. i ="" ="" ="" ="" ,="" zero="" elsewhere.="" in="" each="" case="" find="" the="" mle="" ̂="" of="" .="" also,="" in="" each="" case,="" find="" method="" of="" moments="" estimators="" and="" show="" that="" they="" are="" consistent.="" hint:="" to="" show="" consistency,="" the="" first="" main="" result="" you="" need="" to="" use="" is="" wlln.="" then="" recall="" that="" for="" continuous="" functions="" convergence="" in="" probability="" is="" preserved="" (theorem="" 5.1.4).="" see="" also="" reviews="" that="" are="" posted="" on="" culearn.="" please="" note="" that="" you="" need="" only="" to="" show="" consistency="" of="" method="" of="" moments="" estimators.="">