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Math Help - Advanced Variance solving

  1. #1
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    Question 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!
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  2. #2
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    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.
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  3. #3
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    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
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  4. #4
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    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).
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  5. #5
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    Re: Advanced Variance solving

    Oh god! It is just that simple?
    I'm kind of stupid then Thank you so much!
    Greetings!
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  6. #6
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    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.
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