Question: AssumeX, Y are random variables, defined on some probability space (2, F,P), so that E[|X|] +E[|Y |] < o. Assume E,G CF are o-algebras.

AssumeX, Y are random variables, defined on some probability space (2, F,P),

AssumeX, Y are random variables, defined on some probability space (2, F,P), so that E[|X|] +E[|Y |] < o. Assume E,G CF are o-algebras. A. always, E[Y |G] = E[Y\o(EUG)], P-a.s.; B. if E CG and o(Y) = G, then E[XY|G] = YE[X|G)], P-a.s.; %3D C. if E CG and o(Y) = G, then E[XY|E] = YE[X|E)], P-a.s.; D. if E CG and E # G, then E[X|E] < E[X]G], P-a.s.. Here P-a.s. indicates that, with probability one, an identity or (strict) inequality holds for the associated versions.

Step by Step Solution

★★★★★

3.46 Rating (159 Votes )

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

Document Format (2 attachments)

6363d7850ad89_237507.pdf

180 KBs PDF File

6363d7850ad89_237507.docx

120 KBs Word File

Students Have Also Explored These Related Mathematics Questions!

Show that, if X and Y are random variables taking on only two values each, and if E(XY ) = E(X)E(Y ), then X and Y are independent.

Show that, if X and Y are random variables taking on only two values each, and if E(XY ) = E(X)E(Y ), then X and Y are independent. Discuss.

If two random variables X and Y are defined over a region in the XY-plane that is not a rectangle (possibly infinite) with sides parallel to the coordinate axes, can X and Y be independent?

Suppose that F(x) is a cumulative distribution function. Show that (a) Fn(x) and (b) 1 [1 F(x)]n are also cumulative distribution functions when n is a positive integer. Let X1, . . . ,Xn be...

Let X and Y be two continuous random variables defined over the unit square. What does c equal if fX,Y (x, y)=c(x2 + y2)?

Let {X n ,n = 1, 2,} and {Y n ,n = 1, 2,} be two sequences of random variables, defined on the sample space S. Suppose that we know Prove that X n +Y n L r X +Y . You may want to use Minkowski's...

23. Suppose that F(x) is a cumulative distribution function. Show that (a) F(x) and (b) 1 - [1 - F(x)] n are also cumulative distribution functions when n is a positive integer. HINT: Let X 1 , . ....

Suppose that T and Z are random variables. a. If P(T > 2.02) = 0.05 and P(T 1.64) = P(Z

The administrator of emergency ward of Trinity Hospital has to decide the number of doctors to be made available to treat patients arriving at the facility every night. The number of doctors required...

4. The materials manager of a firm wishes to determine the expected demand for a particular item in stock during the reorder lead time. The information is needed to determine how far in advance to...

SML Suppose you observe the following situation: a. Calculate the expected return on each stock. b. Assuming the capital asset pricing model holds and stock A??s beta is greater than stock B??s beta...

Describe a situation in which a set of audit working papers might be used by third parties to support a charge of gross negligence against the auditors.

In the corn futures contract, the following delivery months are available: March, May, July, September, and December. A company is hedging the purchase of the underlying asset, and the expiration of...

You are evaluating the potential purchase of a small business currently generating $42,500 of after-tax cash flow (D 0 = $42,500). On the basis of a review of similar-risk investment opportunities,...

Chrysler and General Motors vigorously compete with each other in many automobile and truck markets. When Jose Ignacio Lopez was vice president of purchasing for GM, he made it clear that his buyers...

Polly Company purchased three buildings. Polly has assembled the following market data, based on commercial real estate sales in the area in the past six months, which can be used to indirectly...

The comparative temporary investments and inventory balances of a company follow. Current Year Previous Year Temporary investments.........................$44,000..................$40,000...

Lawrence Industries most recent annual dividend was $1.80 per share (D 0 = $1.80), and the firms required return is 11%. Find the market value of Lawrences shares when: a. Dividends are expected to...

how is the function of an epithelium reflected in its arrangement

Answer.... (j) 2 points AssumeX, Y are random variables, defined on some probability space (0, F, P), so that E[IX|] + E[|Y|]

1. A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die. Determine her...

Helpful hint: The following topics/concepts are covered in this homework, in no particular order (different problems cover different concepts): Class 6: Discrete Probability Distributions The...

Need help figuring out the python code for numpy assignment as I am still learning how to write all of the python code. Thank you. Active Experimentation Q1) In the following cell, write the Python...

**Python Language can I get help? **below might help Programming Problem Modify your previous lab to do the following: 1. Using Python, work Ex 9.4 in the lecture notes (Lecture #31, Page 301). Use...

Instuctor's Annotated Edition TENTH EDITION Understandable Statistics Concepts and Methods Charles Henry Brase Regis University Corrinne Pellillo Brase Arapahoe Community College Australia Brazil...