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Math Help - Chebishev

  1. #1
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    Chebishev

    1)
    a dice is being rolled 360 times. the dice has 1 red side and 5 black. what is the upper bound to the probability of falling on a red side more than 41 times and less than 59 times ?

    2)

    X - counts how many times the dice was red, up to 36 times
    Y - counts how many times the dice was red up to 50 times
    find COV(X,Y)

    thanks a million !
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  2. #2
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    isn't there something wrong with the data ???
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by WeeG View Post
    1)
    a dice is being rolled 360 times. the dice has 1 red side and 5 black. what is the upper bound to the probability of falling on a red side more than 41 times and less than 59 times ?
    The mean number of reds on a single roll of a die is \mu_1=1/6, the SD is:

    \sigma^2_1=(1/6)(1-1/6)^2+(5/6)(0-1/6)^2=5/6

    In 360 rolls the mean number of reds is \mu=360 \mu_1=60 and the standard deviation is \sigma=\sigma_1/\sqrt{360}

    Now if the range for the number of reds were 51 to 69 this would now be a straight forward application of Chebyscev's inequality (or if the number of throws were 300 rather than 360).

    I don't think that the 1-sided Chebyshev inequality will work here, so you may have a type.

    CB
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