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Thread: E[Y] and V[Y]

  1. #1
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    E[Y] and V[Y]

    Given random variable X with following probability mass function:
    E[Y] and V[Y]-captura00.jpg
    E[Y] and V[Y]-captura01.jpg
    E[Y] and V[Y]-captura02.jpg
    Last edited by Amanda2018; Oct 25th 2018 at 01:36 PM.
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  2. #2
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    Re: E[Y] and V[Y]

    really?

    $E[Y] = \sum y p[y] = \sum 2^x p[x]$

    $E[Y^2] = \sum y^2 p[y] = \sum 2^{2x} p[x]$

    $V[Y] = E[Y^2] - (E[Y])^2$

    I leave you to do the number crunching
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  3. #3
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    Re: E[Y] and V[Y]

    hi, thanks, i follow those formula,
    E[Y]=2 x 0.3 + 4 x0.5 + 8 x 0.2 = 4.2
    E[Y^2] = 4 x 0.3 + 16 x0.5 + 64x 0.2 = 22
    V[Y]= 22-4.2=17.8
    E[Y] and V[Y]-captura05.jpg

    how i can calculate a, b?
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  4. #4
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    Re: E[Y] and V[Y]

    Quote Originally Posted by Amanda2018 View Post
    hi, thanks, i follow those formula,
    E[Y]=2 x 0.3 + 4 x0.5 + 8 x 0.2 = 4.2
    E[Y^2] = 4 x 0.3 + 16 x0.5 + 64x 0.2 = 22
    V[Y]= 22-4.2=17.8
    Click image for larger version. 

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    how i can calculate a, b?
    You made a mistake in the last line. You forgot to square E[Y]. It should be

    $$V[Y]=22-4.2^2=4.36$$

    For $a,b$ you have $E[Z]=aE[x]+b=0$ and $V[Z]=E[Z^2]-(E[Z])^2=\sum (ax+b)^2p[x]=1$
    Last edited by SlipEternal; Oct 25th 2018 at 04:06 PM.
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