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Math Help - Random Variables

  1. #1
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    Random Variables

    How do I solve this question?

    Q: Let X be a random variable with mean x and standard deviation y. consider a new random variable Z, obtained by subtracting x from X and then dividing the result by y. Use the laws of expected value and variance to prove:
    a) That the expected value of Z= 0
    b) That both the variance and standard deviation of Z are equal to 1.

    Thanks a lot in advance!!
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  2. #2
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    Quote Originally Posted by muffin628 View Post
    How do I solve this question?

    Q: Let X be a random variable with mean x and standard deviation y. consider a new random variable Z, obtained by subtracting x from X and then dividing the result by y. Use the laws of expected value and variance to prove:
    a) That the expected value of Z= 0
    b) That both the variance and standard deviation of Z are equal to 1.

    Thanks a lot in advance!!
    What "laws of expected value and variance" have you been taught. Please list them and then state what your difficulty is in using them.
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  3. #3
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    law of expected value:
    c is a constant. X is a random variable.

    1) E(c)= c
    2) E(X+c)= E(X)+c
    3) E(cX)= cE(X)

    laws of variance:
    1) V(c) = 0
    2) V(X+c) = V(X)
    3) V(cX) = c^2 x V(X)
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  4. #4
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    E\left( {\frac{{X - x}}<br />
{y}} \right) = E\left( {\frac{X}<br />
{y} - \frac{x}<br />
{y}} \right) = \frac{1}<br />
{y}E\left( X \right) - \frac{x}<br />
{y} = ?
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  5. #5
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    Quote Originally Posted by muffin628 View Post
    law of expected value:
    c is a constant. X is a random variable.

    1) E(c)= c
    2) E(X+c)= E(X)+c
    3) E(cX)= cE(X)

    laws of variance:
    1) V(c) = 0
    2) V(X+c) = V(X)
    3) V(cX) = c^2 x V(X)
    Var(aX + b) = a^2 Var(X). In your problem, what is a and what is b ....?
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