Thread: 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!

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.

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

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).

Oh god! It is just that simple?
I'm kind of stupid then Thank you so much!
Greetings!

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.