Welcome to Live Chat

Welcome to LiveWebTutors Services, World's leading Academic solutions provider with Millions of Happy Students.

Call Back
logo

24x7 Support Available

To Get the Best Price Chat With Our Experts

chat now

In A Hurry? Get A Callback

icon
Table of Content

Covariance Assignment Help


Covariance is a term usually associated with random variables. Covariance is a measure of how the change in value of one random variable changes the value of the other random variable. If the increase in value of one random variable increases the value of the other or the decrease in value of one random variable decreases the value of the other, then the covariance is positive. ON the other hand, if the increase in value of one random variable decreases the other, or if the decrease in value of one random variable increases the other, then the covariance is negative .It gives the linear relationship between the two random variables.

An assignment another important factor apart from the sign of the covariance is the magnitude of the value, be it high positive low positive or high negative low negative. The magnitude often tells the strength of the relationship between the two random variables. Calculation of covariance is not a difficult calculation as it involves some expectation terms. Suppose X and Y are to random variables. Then covariance between X and Y is given by: COV(X, Y) =E ((X-E(X)) (Y-E(Y))

The above equation can be modified :COV(X,Y)=E(XY-XE(Y)-YE(X)+E(X)E(Y))=E(XY)-E(X)E(Y).This formula is used very often for calculating covariance .When the random variables X and Y are independent , then E(XY)=E(X) * E(Y).In such cases, the covariance between X and Y is 0.Covariance is also used for calculating the correlation coefficient. The correlation coefficient is a dimensionless quantity. Its value lies between -1 and 1. The correlation coefficient is the ratio of covariance and square root of the product of the variance of X and Variance of Y. Thus the Covariance is less than or equal to square root of the product of the variance of X and Variance of Y because the correlation coefficient is within -1 to 1.


There are several properties of covariance

· COV(X,X)=E(X^2)-E(X)^2

=V(X)

Thus Covariance of random variable with itself is just the variance of the random variable.

· COV(X, a) =0, where a is a constant. Thus the covariance of a random variable with a constant is always 0.

· COY(X, Y) =COV(Y, X) which means the order of the random variable doesn’t matter.

· COV (aX, bY) =abCOV(X, Y). The proof the property is given below:

COV (aX, bY) =E (aXbY)-E (aX) E (bY)

=ab(E(XY)-E(X)*E(Y))

=ab COV(X,Y)

· The above property described the shift of scale property. We now discuss the shift of origin property: COV(X+a,Y+b)=COV(X,Y)

COV(X+a,Y+b)=E((X+a)(Y+b))-E(X+a)E(Y+b)

=E(X *Y+Xb+Ya+ab)-E(X)* E(Y)-E(X)* b-E(Y) *a-a *b

=E(XY) - E(X) *E(Y)

= COV(X,Y)

· Var(X+Y)=V(X)+V(Y)+2cov (X,Y)

When X and Y are independent, then covariance between X and Y IS 0. In such cases, V (X+Y)= V (X) + V (Y)

We have stated that two independent variables have zero covariance but is the converse true? Does zero covariance imply that the random variables are independent? Well infect it does not. If the covariance is zero it just means that there is no linear relationship between the two random variables but they can be dependent on each other in some other way.

So a wise argument is that there might be a dependency of X on Y but they can’t be regarded as independent.

Our Amazing Features
  • On Time Delivery

    There is no deadline that can stop our writers from delivering quality assignments to the students.

  • Plagiarism Free Work

    Get authentic and unique assignments by using our 100% plagiarism-free services.

  • 24 X 7 Live Help

    The experienced team of Live web tutors has got your back at all times of the day. Get connected with our customer support executives to receive instant and live solutions for your assignment problems.

  • Services For All Subjects

    We can build quality assignments in the subjects you're passionate about. Be it Engineering and Literature or Law and Marketing we have an expert writer for all.

  • Best Price Guarantee

    Get premium service at a pocket-friendly rate. At live web tutors, we understand the tight budget of students and thus offer our services at highly affordable prices.

live review Our Mission Client Satisfaction
  • I ordered my HRM assignment from this platform. The solution helped me to pass my assessment with flying colors. Well done! Keep up the good work.

    27 Oct 2020

    Arnisa

  • Recently, I ordered my history case study from this platform. The professionals did great work with the content. I am yet to be graded for it but as far as I reviewed the text I am definitely impressed with the quality provided to me at this price. Thank you for your support.

    27 Oct 2020

    Tammy

  • I got good grades with my nursing assignment, all thanks to the experts of this platform. My writing skills are not that great hence the experts of this portal helped me to pass my program with good grades.

    27 Oct 2020

    Sidorela

  • I ordered my English assignment from this platform. The service was very quick and impressive. The customer support executives were very polite and helpful. I am grateful for their assistance.

    27 Oct 2020

    Jenny

  • Overall, it was a pleasant experience. I ordered my management thesis from this platform. The experts did thorough and detailed work on my assignment. All my instructions were implemented precisely.

    27 Oct 2020

    Fiona

View All Review