Question: Consider the following situation. Let ((, A, P) be a probability space and let X be an integrable r.v. On A, define the (finite) measure

Consider the following situation. Let ((, A, P) be a probability space and let X be an integrable r.v. On A, define the (finite) measure v by v (A) = (A X dP. Then show that v << P if and only if for every ( > 0 there exists ( = ( (() (> 0) such that P (A) < ( implies v(A) < (.

Step by Step Solution

★★★★★

3.47 Rating (180 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Let A n A such that P A n n 0 Then as n PIA n 1 E IA n 1 PA n 0 and therefore X... View full answer

Question Has Been Solved by an Expert!

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

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

742-M-S-P (6857).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

An antihistamine is frequently studied using a model to examine its effectiveness (compared to a placebo) in inhibiting a positive skin reaction to a known allergen. Consider the following situation....

Let X be an integrable r.v. Then, for every ( > 0, there is a simple r.v. X( such that f|X - X(|

Let X be an integrable r.v. and, for B ( A with P(B) > 0, consider the conditional probability on A, P((|B). Then show that Go through the familiar four steps that X is an indicator function, a...

sir, please solve these questions. 5. (12 points) Let ($, F. P) be a probability space. Suppose the price S(t) of a risky asset at time f follows the geometric Brownian motion S(t) = S(0)e(r-! )tow()...

Submitted to Management Science manuscript MS-0001-1922.65 Authors are encouraged to submit new papers to INFORMS journals by means of a style file template, which includes the journal title....

1 Due September 6 Problems 1.20, 1.26, 1.30 from the textbook Add-on sketch of a proof of existence of a set which is not Lebesgue-measurable. The original example is due to G. Vitali. Let = [0, 1);...

(a) How does the use of condition codes complicate the implementation of a superscalar processor that supports out-of-order execution? [4 marks] (b) A branch predictor with a high prediction accuracy...

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)....

I need the code in python For an exercise I'm supposed to write a python code according to the task descriptions they have provided and produce the expected output according to the test cases....

Ryan Ren Assignment Homework 2 due 09/14/2017 at 02:15pm PDT 1. (1 pt) Compute the following product. \u0014 \u0015\u0014 \u0015 \u0014 5 0 4 7 4 = 0 7 1 7 7 Math4A-02-M17-Wen \u0015 Answer(s)...

Ever-Sharp Lawnmowers Ltd. controls variable manufacturing overhead costs with assembly-line hours as the denominator. Fixed manufacturing overhead costs are applied on a unit-of-output basis totals...

When Jack cleans the house, it takes him 4 hours. When Ryan cleans the house, it takes him 6 hours. How long would it take both of them if they worked together?

27. College Admission Test Prep Programs. Three admission test preparation programs are being evaluated. The scores obtained by a sample of 20 people who used the programs provided the following...

The MOST important input into Activity Resource Estimating is: A. The activity list. B. The cost estimates. C. The project charter. D. The constraints and assumptions.

A survey of MBA students obtained the following data on Students first reason for application to the school in which they matriculated. a. Develop a joint probability table using these data. b. Use...

The checking accounts of Sun Bank are categorized by the age of account and the account balance. Auditors will select accounts at random from the following 1000 accounts (numbers in the table are the...

Use the given information to find the number of degrees of freedom, the critical values ? and XR, and the confidence interval estimate of o. It is reasonable to assume that a simple random sample has...

Mr. Bud Green borrowed $10,000 with a promise to repay tire loan in 6 years with a uniform monthly payment and a single payment of $1,000 at the end of six years at a nominal interest rate of 12% per...

Anderson International Limited is evaluating a project in Erewhon. The project will create the following cash flows: Year Cash Flow 0 $585,000 1 215,000 2 158,000 3 223,000 4 202,000 All cash flows...