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    A fair dice is thrown once and the random variable X represents the value on the uppermost face:

    a) Find the mean and variance of X
    b) Calculate the probability that X is within one standard deviation of the mean

    a)

    E(X) = n+1/2 = (6+1)/2 = 7/2 = 3.5

    Var(X) = (n+1)(n-1)/12 = (6+1)(6-1)/12 = 35/12 = 2.92 (3 s.f.)

    b)

    Mean - 1 standard deviation:

    3.5 - (35/12) = 0.583

    Mean + 1 standard deviation:

    3.5 + (35/12) = 6.42

    Probability of it being in this range:



    =P(0.583.......<R< 6.42) = P(1 =/< R =/< 6)


    How do I find the probability? Help please!
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    (Original post by Mambo No. 5)
    A fair dice is thrown once and the random variable X represents the value on the uppermost face:

    a) Find the mean and variance of X
    b) Calculate the probability that X is within one standard deviation of the mean

    a)

    E(X) = n+1/2 = (6+1)/2 = 7/2 = 3.5

    Var(X) = (n+1)(n-1)/12 = (6+1)(6-1)/12 = 35/12 = 2.92 (3 s.f.)

    b)

    Mean - 1 standard deviation:

    3.5 - (35/12) = 0.583

    Mean + 1 standard deviation:

    3.5 + (35/12) = 6.42

    Probability of it being in this range:



    =P(0.583.......<R< 6.42) = P(1 =/< R =/< 6)


    How do I find the probability? Help please!
    You may want to check you're calculation of the S.D. again...
    Try using: Var(X) = E[X^2] - [(E[X])^2]
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    (Original post by XShmalX)
    Is it not just 1 as R could be 1,2,3,4,5 or 6?
    The answer in the book is 2/3 . Any ideas?
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    (Original post by XShmalX)
    Is it not just 1 as R could be 1,2,3,4,5 or 6?
    My variance calculation is right, the book's answers confirm it.
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    (Original post by Mambo No. 5)
    My variance calculation is right, the book's answers confirm it.
    But you need to square root it to get the standard deviation so S.D=1.7018... which gives a smaller range of values.
    ie. 2-5 so P=4/5=2/3
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    (Original post by XShmalX)
    But you need to square root it to get the standard deviation so S.D=1.7018... which gives a smaller range of values.
    ie. 2-5 so P=4/5=2/3
    Thank You. +1rep
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    (Original post by Mambo No. 5)
    Thank You. +1rep
    Thanks! You're most welcome!
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    Sorry I still don't get the b part.
 
 
 
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