Question: Let (0, , P) be a probability space and let F and & be two sub-o- algebras of . Suppose that they are independent, and

Let (0, , P) be a probability space and let F and & be two sub-o- algebras of . Suppose that they are independent, and suppose that X is real valued random variable on ? which is measurable with respect to both F and . Show that X is a.s. constant; that is there is real number c E R so that P(X = c) = 1

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 Mathematics Questions!

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...

Independence (2). Let \((\Omega, \mathscr{A}, P)\) be a probability space and assume that the \(\sigma\)-algebras \(\mathscr{B}, \mathscr{C} \subset \mathscr{A}\) are independent (see Problem 5.11)....

For monotone functions f, f0: P Q between posets (P, vP ) and (Q, vQ), let f v f(i) Prove that the binary relation v is a partial order. [3 marks] (ii) For monotone functions between posets p : P 0...

Return to the Sport Hotel example in the course notes, the lesson, and in Chapter 9. Suppose that everything stays the same as was presented in the original problem, except one thing -- the value of...

Hi! Help me please Problem 2. Intertemporal choice Mainy Landin has an income of 200.000 kr this year and she expects an income of 110.000 kr next year. She can borrow and lend money at an interest...

Let (, F, P) be a probability space of infinite coin independent tosses, with = (12....) . Assume that P(i = H) = p, and P(i = T) = 1 p, with p (0, 1). Problem 1. Let (0, F, P) be a probability space...

Let (, F, P) be a probability space. A finite collection of events A1, ..., Ak satisfy the 'product rule iff P A1 A2 ... Ak = Q j=1..k P Aj . An arbitrary collection of events are called independent...

Stat 401: Applied Statistical Methods II Fall 2016 Homework #3 Due Date: October 7 (in your lab) 1. An exam has two questions. Let (X, Y) be the outcomes for a randomly selected student. X = 1 if the...

7. Let (, F, P) be a probability space. We consider a symmetric random walk such that the j-step is defined as Zj = :{ 1 with probability 1/2 -1 with probability 1/2 where Zi and Z; are independent,...

Stats 120B Homework 4: Due Thursday, Feb. 11 1. Let X and Y be two i.i.d random variables following N (3, 1). (a) Find the distribution of 2X + Y using any method you like. (b) Find the distribution...

For each of the problem, state whether it is true or false. a. Fixed cost problem is a common example of mixed integer programming. b. Mutually exclusive constraints require both variables to be...

Steve Kilmeade is the Export Manager at Braveheart Industries, a manufacturer of office furnishings. He has identified Russia as a promising market and decides to attend a furniture trade fair in...

13.78 An analyst has the objective of predicting the return on average tangible common equity (ROATCE) of banks. The analyst begins by using efficiency ratio, a measure of a banks ability to turn...

Create a 1-page matrix or table to describe your action plan for each of the three changes that you plan to make, per "Self-confidence, Positive mindset, Emotional Intelligence" Please list the 3...

2. In this chapter, the reader should reflect on the following concepts: Basic values, basic interests, position, socialization process, mental variables and norm distribution.

6. List examples from your local environment of people that have a so-called Protestant character. Add further characteristics to this phenomenon than those mentioned in this chapter.

10. Choose someone you know and answer the following questions: a) Does this person have a low or high level of competence in a particular field? b) Do you have a low or high level of confidence in...