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Thread: variance of a function of random variables

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    variance of a function of random variables




    Hi all,

    I'm trying to calculate the variance of a function of two continuous random variables and could do with a nudge in the right direction seeing as its been a good few years since I did any probability theory work. You may also notice that my latex is a little ropey too...

    Specifically I need to calculate var(z):

    z = x-y, x>y
    z= 0, x<y

    where x and y are both iid uniform(a,b)

    If it helps:
    E(z|x)=\frac{(x-a)^2}{2(b-a)}
    E(z)=\frac{b-a}{6}
    var(z|x)=\frac{(x-a)^3}{3(b-a)}-\frac{(x-a)^4}{4(b-a)^2}

    Is the law of total variance relevant? Any help greatly appreciated

  2. #2
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    Re: variance of a function of random variables


    Without investigating any good tricks to solve this problem, you can always refer back to the fundamental definition:

    Var[Z] = E[Z^2] - E[Z]^2

    = \int_a^b \int_y^b \frac {(x - y)^2} {(b - a)^2} dxdy- E[Z]^2

    provided that you already calculated E[Z]

  3. The Following User Says Thank You to BGM For This Useful Post:

    james92 (07-11-2015)

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