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Math Help - 10 Sided Die

  1. #1
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    10 Sided Die

    Say we have a ten sided die.

    Teacher wants us to find the prob mass function. Thats easy... f(u)=1/10 for 1,2,3,4,5,6,7,8,9,10.

    We know E(U) is the mean = 5.5

    How do we figure out something like...

    E(2U-7)

    or

    E(U^2 +4)
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    Quote Originally Posted by DINOCALC09 View Post
    Say we have a ten sided die.

    Teacher wants us to find the prob mass function. Thats easy... f(u)=1/10 for 1,2,3,4,5,6,7,8,9,10.

    We know E(U) is the mean = 5.5

    How do we figure out something like...

    E(2U-7)

    or

    E(U^2 +4)
    E(aX + b) = a E(X) + b.

    E(U^2 + 4) = E(U^2) + 4. To get E(U^2) you first need to construct the pmf of U^2 from the pmf of U.
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    Are the answers 4.0 and 42.5 respectively?
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    Quote Originally Posted by DINOCALC09 View Post
    Are the answers 4.0 and 42.5 respectively?
    I don't do arithmetic. If you post working that clearly shows where these answers have come from, someone will tell you if the working is OK (and, one would assume, if the working is OK then the answers will be OK).
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    we know E(U) = 5.5

    So E(2U-7) = 2E(U)-7 = 2*5.5-7 = 4


    Then E(U^2 + 4) = E(U^2)+4 = [(n+1)(2n+1)]/6 + 4 = 38.5 + 4 = 42.5

    THANKS
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    Quote Originally Posted by DINOCALC09 View Post
    we know E(U) = 5.5

    So E(2U-7) = 2E(U)-7 = 2*5.5-7 = 4


    Then E(U^2 + 4) = E(U^2)+4 = [(n+1)(2n+1)]/6 + 4 = 38.5 + 4 = 42.5 Mr F says: This line does not (for me at least) satisfy my request "... post working that clearly shows where these answers have come from". I doubt your instructor would be too happy with it either.

    THANKS
    ..
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    formula in the book after manipulating the variance forumula.

    [1^2 + 2^2 + ... + n^2]/n

    [n(n+1)(2n+1)]/6n

    [(n+1)(2n+1)]/6

    (n^2 -1)/12

    10 sides of a die, hence n = 10
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    Quote Originally Posted by DINOCALC09 View Post
    formula in the book after manipulating the variance forumula.

    [1^2 + 2^2 + ... + n^2]/n

    [n(n+1)(2n+1)]/6n

    [(n+1)(2n+1)]/6

    (n^2 -1)/12 Mr F says: I have no idea where this line has come from.
    10 sides of a die, hence n = 10
    Your work, although poorly set out, appears to be correct. Your answers look OK.
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