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Math Help - [SOLVED] Mean question

  1. #1
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    [SOLVED] Mean question

    Hello, i am stuck on a question and i can't work it out.

    if you have the number 1234, and you take all 24 permutations of it, you let X = the number of numbers that stay the same i.e 1324 = X=2 as 1 and 4 have stayed teh same, 4321 = X=0 as none have stayed the same.

    Now the question says that E(X) = 1, yet when i work it out i get 2

    X = {0,1,2,3,4} so E(X) = ((0+1+2+3+4)/5) = 2

    where am i going wrong?
    Last edited by mr fantastic; June 4th 2009 at 09:20 PM. Reason: Restored question deleted by OP
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  2. #2
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    Quote Originally Posted by Rapid_W View Post
    Hello, i am stuck on a question and i can't work it out.

    if you have the number 1234, and you take all 24 permutations of it, you let X = the number of numbers that stay the same i.e 1324 = X=2 as 1 and 4 have stayed teh same, 4321 = X=0 as none have stayed the same.

    Now the question says that E(X) = 1, yet when i work it out i get 2

    X = {0,1,2,3,4} so E(X) = ((0+1+2+3+4)/5) = 2

    where am i going wrong?
    Hi Rapid W,

    It is true that the possible values of X are 0, 1, 2, 3, and 4, but it is not true that they are all equally likely (which is what you seem to assume).

    Suggestion: Write down all 24 permutations of 1234, then write down the value of X for each permutation. Then compute the average value of X.
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  3. #3
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    crikey i completely forgot they they had different probablitys X=3 doesn't even occur. Thank you for pointing ou the obvious
    Last edited by mr fantastic; June 4th 2009 at 09:20 PM. Reason: Restored post deleted by OP
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  4. #4
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    mean = ((1/24)*4)+((6/24)*2)+(8/24) = 1

    am i correct in therefore thinking that the variance is -4/5 ?
    Last edited by mr fantastic; June 4th 2009 at 09:23 PM. Reason: Restored question deleted by OP.
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  5. #5
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    Quote Originally Posted by Rapid_W View Post
    mean = ((1/24)*4)+((6/24)*2)+(8/24) = 1

    am i correct in therefore thinking that the variance is -4/5 ?
    ? No, the variance can never be negative.
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