Advanced Variance solving

Hey!

I have some variance problems, that I hope you can help me solving - here we go:

"Given that var X = var Y = cov (X,Y) = 1, find

a) Var(3-X)

b) Var (2X+4)

..."

I just want to get started. I've checked all of the statistics book, that we have at college, and it really won't be solved ;) The answer to these to problems are:

"a) 1

b) 4"

I just want to now which formula, I should use - I have look everywhere now :(

Thank you in advance! ;)

Re: Advanced Variance solving

Hey MartinDalskov.

For these expressions, there is a well known one for variance and with two variables we have:

Var[X+Y] = Var[X] + Var[Y] + 2*Cov(X,Y) with

Var[aX] = a^2*Var[X] and

Var[X+c] = Var[X] for some constant c.

If X and Y are independent then Cov(X,Y) = 0 but if not you must include this term.

Re: Advanced Variance solving

Hi again.

Yes, I've tried that for about two hours now - Both way around. It just won't give 1 ;) Not in my world ;)

Could you insert it, in the correct order for me? Just the a one?

I'm close to frustrated about this ;)

Re: Advanced Variance solving

Recall Var[-X] = (-1)^2Var[X] = Var[X].

Var[3-X] = Var[-X] = Var[X].

The second one is very similar (using the same kind of rules).

Re: Advanced Variance solving

Oh god! ;) It is just that simple? ;)

I'm kind of stupid then ;) **Thank you so much!**

Greetings!

Re: Advanced Variance solving

Don't stress too much.

A lot of mathematics is like this, and what typically happens is that we get a list of rules that other people prove and we just a find way to use them to do what we need.

Kind of like the difference between engineers and scientists or pure mathematicians vs applied mathematicians.