Question: 9.16 (i) Show that for any random variable X, E X2{log(|X|)}d1 log log(|X|) < , where d > 1, implies E(X2) < .

9.16 (i) Show that for any random variable X, E



X2{log(|X|)}d−1 log log(|X|)



< ∞, where d > 1, implies E(X2) < ∞.

(ii) Give an example of a random variable X such that E X2 log log(|X|)
< ∞
but E(X2)=∞.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Principles Of Managerial Statistics Questions!

Q:

With reference to Ex. 10.4 (a) Apply Eq. (10.7) to Eq. (A) to verify Eqs. (B) and (C). (b) Show that Eqs. (B) and (C) combine in accord with Eq. (10.11) to regenerate Eq. (A). Eq. (10.11) (c) Show...

Q:

2.1 Marginal and conditional probability: The social mobility data from Sec- tion 2.5 gives a joint probability distribution on (Y1, Y2)= (father's oc- cupation, son's occupation). Using this joint...

Q:

Exercises Chapter 2 2.1 Marginal and conditional probability: The social mobility data from Section 2.5 gives a joint probability distribution on (Y1 , Y2 )= (father's occupation, son's occupation)....

Q:

Briefly describe ASCII and Unicode and draw attention to any relationship between them. [3 marks] (b) Briefly explain what a Reader is in the context of reading characters from data. [3 marks] A...

Q:

STAT 200: Introduction to Statistics Final Examination Spring 2017 OL /US2 Page 1 of 6 STAT 200 OL4/US2 Sections Final Exam 201 The final exam will be posted at 12:01 am on Ma , 2 7 and it is due at...

Q:

QUIZ... Let D be a poset and let f : D D be a monotone function. (i) Give the definition of the least pre-fixed point, fix (f), of f. Show that fix (f) is a fixed point of f. [5 marks] (ii) Show that...

Q:

MUST BE CORRECT ANSWERS A small software company has the following simplified cashflow, funded by shareholders' equity of 20,000 and a bank overdraft of 5000: Invoiced money received 2 months after...

Q:

MATH S350 TMA 01 Hints Question 1 Let A and B be the event that water is contaminated with excessive amount of pollutant A and pollutatnt B respectively. Remarks: 1. Half of those communities whose...

Q:

Miller-Rabin test to check whether a number N is composite. This will involve computing a N1 mod N for some value of a. [10 marks] Carry out the steps for N = 65 and a = 1, 2, 8 and 12. on what each...

Q:

MATHEMATICS FOR MACHINE LEARNING Marc Peter Deisenroth A. Aldo Faisal Cheng Soon Ong Contents Foreword 1 Part I Mathematical Foundations 9 1 Introduction and Motivation 11 1.1 Finding Words for...

Q:

Write an alternative definition that is tail-recursive (iterative) and makes use of accumulator variables. [10 marks] Explain why your alternative definition executes more efficiently. [3 marks] 1...

Q:

Prodoc Editors Ltd (PEL) is a medium-sized firm specialising in the provision of technical writing services. From their offices in Christchurch, Wellington and Auckland, PEL's specialist writers...

Q:

WindMill Ltd. is a Spanish transportation and distribution company focused on the transportation of food to supermarkets.Calefull, a supermarket company, is one of WindMill's largest customers and...

Q:

Refer to the information for Solpoder Corporation. Solpoder Corporation has the following comparative financial statements: Dividends of $17,100 were paid. No equipment was purchased or retired...

Q:

Server farms such as Google and Yahoo! provide enough compute capacity for the highest request rate of the day. Imagine that most of the time these servers operate at only 60% capacity. Assume...