Question

How do you know that the determinant of a variance-covariance matrix must be greater than or...

How do you know that the determinant of a variance-covariance matrix must be greater than or equal to zero? The answer is one short sentence. (

Let x and y be scalar random variables. Recall Corr(x, y) = √ Cov(x,y) . Using V ar(x)V ar(y) what you have shown about the determinant, show −1 ≤ Corr(x,y) ≤ 1.

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Calculate the quantity of interest please. a) Let X,Y be jointly continuous random variables generated as...
Calculate the quantity of interest please. a) Let X,Y be jointly continuous random variables generated as follows: Select X = x as a uniform random variable on [0,1]. Then, select Y as a Gaussian random variable with mean x and variance 1. Compute E[Y ]. b) Let X,Y be jointly Gaussian, with mean E[X] = E[Y ] = 0, variances V ar[X] = 1,V ar[Y ] = 1 and covariance Cov[X,Y ] = 0.4. Compute E[(X + 2Y )2].
True or false? and explain please. (i) Let Z = 2X + 3. Then, Cov(Z,Y )...
True or false? and explain please. (i) Let Z = 2X + 3. Then, Cov(Z,Y ) = 2Cov(X,Y ). (j) If X,Y are uncorrelated, and Z = −5−Y + X , then V ar(Z) = V ar(X) + V ar(Y ). (k) Let X,Y be uncorrelated random variables (Cov(X,Y ) = 0) with variance 1 each. Let A = 3X + Y . Then, V ar(A) = 4. (l) If X and Y are uncorrelated (meaning that Cov[X,Y ] =...
Let X1, X2 be two normal random variables each with population mean µ and population variance...
Let X1, X2 be two normal random variables each with population mean µ and population variance σ2. Let σ12 denote the covariance between X1 and X2 and let ¯ X denote the sample mean of X1 and X2. (a) List the condition that needs to be satisfied in order for ¯ X to be an unbiased estimate of µ. (b) [3] As carefully as you can, without skipping steps, show that both X1 and ¯ X are unbiased estimators of...
Let (X,Y) be a two dimensional Gaussian random vector with zero mean and the covariance matrix...
Let (X,Y) be a two dimensional Gaussian random vector with zero mean and the covariance matrix {{1,Exp[-0.1},{Exp[-0.1],1}}. Calculate the probability that (X,Y) takes values in the unit circle {(x,y), x^2+y^2<1}.
Suppose that the joint probability density function of the random variables X and Y is f(x,...
Suppose that the joint probability density function of the random variables X and Y is f(x, y) = 8 >< >: x + cy^2 0 ≤ x ≤ 1, 0 ≤ y ≤ 1 0 otherwise. (a) Sketch the region of non-zero probability density and show that c = 3/ 2 . (b) Find P(X + Y < 1), P(X + Y = 1) and P(X + Y > 1). (c) Compute the marginal density function of X and Y...
For this question, you may (where appropriate) write down an Excel formula using one of the...
For this question, you may (where appropriate) write down an Excel formula using one of the functions listed below instead of providing a numerical answer. However, you must specify clearly the value of each parameter in the Excel function (you may use the 2010 or the 2007 version). If you choose to provide a numerical answer, it should be accurate to 3 significant figures. (a) Let F denote the cumulative distribution function (cdf) of a uniformly distributed random variable X....
1) Probability assumes you know the sample statistics. TRUE/FALSE 2) Let the support of X contain...
1) Probability assumes you know the sample statistics. TRUE/FALSE 2) Let the support of X contain the values {-1,1}. Let the support of Y contain the values {-1000,1000}. True or false: the expectation of X equals the expectation of Y. For both X and Y assume the probabilities for both events are equal. P(X=-1) = 0.5, P(X=1) = 0.5, P(Y=-1000) = 0.5, P(Y=-1000) = 0.5 3)Let the support of X contain the values {-1,1}. Let the support of Y contain...
True or False: 10. The probability of an event is a value which must be greater...
True or False: 10. The probability of an event is a value which must be greater than 0 and less than 1. 11. If events A and B are mutually exclusive, then P(A|B) is always equal to zero. 12. Mutually exclusive events cannot be independent. 13. A classical probability measure is a probability assessment that is based on relative frequency. 14. The probability of an event is the product of the probabilities of the sample space outcomes that correspond to...
Let X be a normal random variable with ?=−10 and ?=2. Let Z be a standard...
Let X be a normal random variable with ?=−10 and ?=2. Let Z be a standard normal random variable. Draw density plots for both random variables on the same graph. You will want an x-axis that goes from around -20 to around 5. Your y-axis will start at zero and will need go high enough to cover the highest density. Recall that the density of a normal random variable at the point ? with mean ? and standard deviation ?...
1. Suppose that you have a sample of 500 observations on two random variables: price denoted...
1. Suppose that you have a sample of 500 observations on two random variables: price denoted as X, and profit, denoted as Y. So you observe {xi, yi} for i=1,...500. Write down the formula for sample mean and sample variance of X and Y as well as the sample covariance between X and Y. 2. Let Y denote the average starting salary for 2014 U.S. college graduates, measured in dollars. Suppose that the average annual salary is $56,000 dollars, with...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT