Math Is Fun Forum

pinto89

Member

Registered: 2011-10-23

Posts: 2

Variance

Sort of stupid question, but how do you find Var(mX + nY -oZ), where the lower case letters are constants and upper case letter are random variables?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: Variance

hi pinto89

Not stupid at all.  The minus makes no difference;  formula is the same either sign; you always add the bits ;

it does assume the variables are not correlated.

Bob

Last edited by Bob (2011-10-24 00:14:33)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

pinto89

Member

Registered: 2011-10-23

Posts: 2

Re: Variance

Hi bob!
Could you please describe why there are no covariances?
Thanks!

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: Variance

hi pinto89,

I'll have a go.  I'll show a proof with just two variables, X and Y.

let

I'm avoiding using 'n' here because I want that for the number of data items.

So CoVariance is there. 

However, if X and Y are independent variables CoVar(X,Y) = 0

in which case

And now my brain hurts     so I'll need a while before you ask the next question.  Maybe, that's all clear??? 

Bob

Last edited by Bob (2011-10-24 06:57:35)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob