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Math Help - Var(Y)

  1. #1
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    Var(Y)

    Y is the present-value random variable of an annuity that pays 1 at the beginning of each year that (x) survives.
    You are given:
    (i) E(Y) @ delta = 10
    (ii) E(Y) @ 2delta = 6.
    (iii) i = 1/24

    Calculate the variance of Y.


    The equation for the Var(Y) to use is 1/d2 * [(^2)A_x Ė A_x^2]
    (Excuse the notation the 2's are raised and the x's are subscripts)
    I got 1/d^2 to be 625 and I thought (i) was saying that A_x = 10 and (ii) that (^2)A_x = 6, but plugging these values in doesnít return the right answer. Does anyone know what Iím doing wrong? Thanks!
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  2. #2
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    Close

    Hey,
    He gave us the formula 1=d(a_doubledot x)+Ax
    Thats how we get Ax.

    the 10 is equal to the a_doubledot x

    So when I work that out, I get Ax=.6, but I don't know how to get the other part of that. I got the 625 to though.

    Let me know if you get it.
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  3. #3
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    One more thing

    To get the other part, try doubling the i, when I work it out, I get 111.53.

    Close, any thoughts?
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  4. #4
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    Ohh thanks for the help I got the last part!

    delta = ln(1 + 1/24) = .040822
    So 2delta = .081644 = ln(1 + i) , so i = .085069 and d = .0784
    And 2A_x = 1 - d*6 = .5296
    Andd then you get 106 when you plug it in
    Thanks again!
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