Question: Prove that if Var(X) < and Var(Y) < , then Cov(X, Y) is finite. By considering the relation [(X X) (Y

Prove that if Var(X) < ∞ and Var(Y) < ∞, then Cov(X, Y) is finite. By considering the relation [(X − μX) ± (Y − μY)]2 ≥ 0, show that
|(X − μX)(Y − μY )| ≤ 1/2 [(X − μX)2 + (Y − μY )2].

Step by Step Solution

★★★★★

3.25 Rating (169 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

We shall follow the hint given in this exercise The ... 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)

602-M-S-C-R-V (1501).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Prove that if E[Y|X = x] = E[Y] for all x, then X and Y are uncorrelated; give a counterexample to show that the converse is not true. Prove and use the fact that E[XY] = E[XE[Y|X]].

The method of control variates is a technique for reducing the variance of a simulation estimator. Suppose that we wish to estimate Î¸ = E(W). A control variate is another random variable...

The method of antithetic variates is a technique for reducing the variance of simulation estimators. Antithetic variates are negatively correlated random variables that share a common mean and common...

Please show complete steps. (a) determine the constant c so that f(x, y) satisfies the conditions of being a joint pmf for two discrete random variables X and Y; (b) compute the marginal pmfs of X...

QUESTION 1 "With the Date object, getTime() returns the number of milliseconds since January 1, 1970" True False 2 points QUESTION 2 Using magic numbers in your code is a good practice. True False 2...

Statistics Project Problem: Consider one way of modeling a problem. Say you have a device an in any given year there is about a 1 in 6 chance that the device will fail. A question is, \"On average,...

A comparative study is performed; you are given the following information. ? The total number of subjects equals 29. ? The observed value of the test statistic is greater than 0. I used the website...

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...

I need help to all the questions in the document attached. I'm trying to study for my final that is 1 day and these are crucial for me. Investment Management 333-693 Final Examination Seat No:...

I would like the solutions for questions #2 & #14 w eTextbooks | Rentor Bu a xiG 1 G L X Bookshelf Online: An Int 2. with s 1-R 3, 5, 7)o With S1-2 3, 5, 7} and > 0...

Suppose that you are testing the hypotheses H0: = 80 vs. HA: 80. A sample of size 61 results in a sample mean of 75 and a standard deviation of 1.5. a) What is the standard error of the mean? b)...

1. For potential flow, the velocity potential is related to the velocity field as follows: V = - Vo. For potential flow around a sphere, & is given by the following Q = -V R 2r -cose +rcose where V...

1. The cost of a machine is Rs 400,000/-. The annual maintenance cost is Rs 40,000 in the first year and it increases by 10% in every subsequent year. The scrap value of the machine at the end of its...

2. How do we define a stock's alpha, and w hat is its interpretation?

For any events A and B with P(B) > 0, show that P(A | B) + P(A | B) = 1.

If P(B|A) > P(B), show that P(B | A)

Show that for any three events A, B, and C with P(C) > 0, P(A B|C) = P(A|C) + P(B|C) - P(A B|C).

7. Suppose you would like to invest $5000 into a mutual fund for three years. The following 3 mutual fund all have an expected annual return of 12% but with different fee structures. Which mutual...

3 Part Question Jakes Car-Buying Decisions Jake, who lives in St. Louis, is trying to decide between the following car models: Brand and Model Cost Hyundai Accent $14,195 Mini Cooper 23,450 Jeep...

Integer Optimization/Optimization. Use Excel to build an LP model , then use the solver to solve questions. In your Excel file, besides your data sheets , you need to have a designated sheet only for...