Question: 4. Let g(.) be a function satisfying g(x) > 0 for x > 0, g(x) increasing for x > 0, and E|g(X)| } < Eg(|X|)

4. Let g(.) be a function satisfying g(x) > 0 for x > 0, g(x) increasing for x > 0, and E|g(X)| <∞. Show that P{|X| > ε} <

Eg(|X|)

g(ε)

for every ε > 0.

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 Introduction To Probability Statistics Questions!

Q:

Using the following attached reading titled "An Institutional Explanation of the Democratic Peace by Bruce Bueno de Mesquita, James D. Morrow, Randolph M. Siverson and Alastair Smith compose a paper...

Q:

answer all questions as instructed below. make sure you have attended all questions .Comparative Architectures (a) Describe the organisation of a two-level branch predictor that makes use of a global...

Q:

1. If f is the function given by f (x) = - + 5x - 1, then f'(2) = X (A) 4 (B) 6 (C) 7 (D) 11 2 . [be 3x dx = (A) 203* + C (B) 6ex + C (C) 18ex + C 63x+1 (D) + C 3x + 14. lff'(x) = 3x2+ 2x and f(2) =...

Q:

ASSIGNMENT #A 2008 BCS No Calculator (AB use a Calculator) 5. The derivative of a function f is given by S'(x) = (x - 3)et for & > 0, and / (1) = 7. (a) The function f has a critical point at x = 3....

Q:

1. If f(x) = sin(e-*) then f'(x) = 2. If f (x) = -x3 + x+ = thenf'(-1) = 3. [cos'(x3)] = 4. If f(x) = tan(2x) then f' () = 5. Let f(x) be the function satisfying f'(x) = x /f(x) for all real numbers...

Q:

please answer all the questions correctly with a small explanation for each question :) QUESTION 1 x'+3132x+7 Let g be the function 9(1): cm x ' Applying the [VT to g on the interval [2r 1]...

Q:

4. Let f be a function with domain (-co, 0) U (0, co). Prove that IF lim f (x) = 00 x-+0 THEN lim f(x) does not exist x-+0 Notes: Before you write this proof, make sure you understand the precise...

Q:

prove by using the same format and method as the example 4. Let f be a function with domain (-co, 0) U (0, co). Prove that IF lim f (x) = 00 x-+0 THEN lim f(x) does not exist x-+0 Notes: Before you...

Q:

9. Let f be a differentiable function with / (2) = 3 and f "(2) - -5, and let g be the function defined by (x) = x/(x). Which of the following is an equation of the line tangent to the graph of g at...

Q:

(iii) Now express your decision rule instead using only the quantities p(Ck), p(Cj ), p(x|Ck), p(x|Cj ), and relate it to the diagram above. [2 marks] (iv) If the classifier decision rule assigns...

Q:

Use Fishers LSD method to analyze the five means for the coating types described in Exercise 13-5. Use a = 0.01.

Q:

Sales Manager Rachel Tabak of Johnson Inc. is in the process of analyzing the sales results for March. March results follow: Units Sales Price Revenue Budget Amounts 20,000 $40 $800,000 Actual...

Q:

Jeff opens a walk - in dental clinic in Zhuhai. The clinic offers two main services: Routine Check - ups and Teeth Whitening. The following is the operating performance for the first quarter in 2 0 2...

Q:

The lack of innovation and entrepreneurial focus at American Express (AmEx) may be because of hubris, inertia, and a lack of capability. The firms performance in 2014 was not, by any means, what...

Q:

Let X Uniform (0, 1). Suppose that given X = x, Y and Z are independent and Y |X = x Uniform(0,x) and Z|X = x Uniform(0, 2x). Define the random vector U as 1. Find the PDFs of Y and Z. 2. Find the...

Q:

Let X be an n-dimensional random vector. Let A be a fixed (non-random) invertible n by n matrix, and b be a fixed n-dimensional vector. Define the random vector Y as Y = AX +b. Find the PDF of Y in...

Q:

Let be a normal random vector with the following mean and covariance matrices Let also 1. Find P(X 2 > 0). 2. Find expected value vector of Y, m Y = EY. 3. Find the covariance matrix of Y, C Y . 4....

Q:

Find the angle between the vectors. (First find an exact expression and then approximate to the nearest degree.) u-i- 6j+k, v = -2i+j+ 3k exact approximate o

Q:

Instructions The following payments and receipts are related to land, land improvements, and buildings acquired for use in a wholesale ceramic business. The receipts are identified by an asterisk...

Q:

THOMAS TECHNOLOGIES CORP. Thomas Technologies Corp. (TTC) is an engineering services company based in Calgary. The company's Class B common shares are listed on the Toront Thomas, the company...