answersLogoWhite

0


Best Answer

var(x) = E[(x - E(x))2]

= E[(x - E(x)) (x - E(x))] <-------------Expand into brackets

= E[x2 - xE(x) - xE(x) + (E(x))2] <---Simplify

= E[x2 - 2xE(x) + (E(x))2]

= E(x2) + E[-2xE(x)] + E[(E(x))2]

= E(x2) - 2E[xE(x)] + E[(E(x))2] <---Bring (-2) constant outside

= E(x2) - 2E(x)E[E(x)] + E[(E(x))2] <--- E[xE(x)] = E(x)E(x)

= E(x2) - 2E(x)E(x) + [E(x)]2 <----------E[E(x)] = E(x)

= E(x2) - 2[E(x)]2 + [E(x)]2

var(x) = E(x2) - [E(x)]2

User Avatar

Wiki User

15y ago
This answer is:
User Avatar

Add your answer:

Earn +20 pts
Q: How do you Derive variance formula?
Write your answer...
Submit
Still have questions?
magnify glass
imp
Related questions

How do you derive variance of Pareto distribution?

var(X) = (xm/a - 1)2 a/a-2 . If a &lt; or equal to 2, the variance does not exist.


What is the formula for calculating variance and standard deviation?

b-a/6


How do you derive the formula of ozone layer?

Ozone layer has no formula. However there is a formula for ozone and that is O3.


What is a sentence using the word derive?

The mathematician spent all day trying to derive the complex formula.


How do you derive work done formula?

The answer depends on what information you have.


How do you find variance?

You calculate it using the appropriate formula, which, given the limitations of this site, is not easy to reproduce. However, you can easily Google the formula.


How do you derive formula for finding the denominator of lapsac fraction?

Classic IB student...


How do you derive the formula of finding the area of a trapezium?

It is: 0.5*(sum of its parallel sides)*height


Derive recursion formula for sin by using Taylor's Series?

the Taylor series of sinx


How can you derive a formula for the area of a trapezoid?

Area = 0.5*(sum of parallel sides)*height


When do we use the unbiased formula of variance?

Variance is a characteristic parameter of a probability distribution: it is not a statistic. In any particular situation (with a few strange exceptions) it has only one value and therefore cannot have any bias.


When you have budjeted amount actual accrued and actual expended amount then formula for budget variance?

I have NO idea what your asking but Sure :) You can.