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Math Help - Discrete Random Variable

  1. #1
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    Discrete Random Variable

    The median annual income for the heads of households in a certain city is $44,000. Four such heads of households are randomly selected for inclusion in an opinion poll. Let X be the number (out of four) who have annual incomes below $44,000.

    Find the probability distribution.

    \displaystyle\frac{\binom{4}{x}\binom{4}{4-x}}{\binom{y}{4}}, \ \ \ x=0, \ 1, \ 2, \ 3, \ 4

    I don't know what y is.
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  2. #2
    Super Member Random Variable's Avatar
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    Notice that they said "median" and not "mean." So it's binomial with p = 0.5 and n = 4.
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    Grand Panjandrum
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    Quote Originally Posted by dwsmith View Post
    The median annual income for the heads of households in a certain city is $44,000. Four such heads of households are randomly selected for inclusion in an opinion poll. Let X be the number (out of four) who have annual incomes below $44,000.
    As Random_Variable points out this is a binomial RV with p=0.5 and n=4 (because $44,000 is the median)

    Find the probability distribution.

    \displaystyle\frac{\binom{4}{x}\binom{4}{4-x}}{\binom{y}{4}}, \ \ \ x=0, \ 1, \ 2, \ 3, \ 4

    I don't know what y is.
    This last part makes no sense is it supposed to be related to the first part? How?

    CB
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    Quote Originally Posted by CaptainBlack View Post
    As Random_Variable points out this is a binomial RV with p=0.5 and n=4 (because $44,000 is the median)



    This last part makes no sense is it supposed to be related to the first part? How?

    CB
    The probability distribution p(x) is for x = 0, 1, 2, 3, 4.

    So my numerator would be 4 choose x times the 4 choose 4-x divided by the sample population which would be population choose 4 but I don't know the population.
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    Grand Panjandrum
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    Quote Originally Posted by dwsmith View Post
    The probability distribution p(x) is for x = 0, 1, 2, 3, 4.

    So my numerator would be 4 choose x times the 4 choose 4-x divided by the sample population which would be population choose 4 but I don't know the population.
    That is not the mass function for the binomial distribution.

    CB
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  6. #6
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    Quote Originally Posted by CaptainBlack View Post
    That is not the mass function for the binomial distribution.

    CB
    Then I don't know what I am supposed to do.
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  7. #7
    Grand Panjandrum
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    Quote Originally Posted by dwsmith View Post
    Then I don't know what I am supposed to do.
    As we have said $$X is a RV with a binomial distribution B(p=0.5, n=4)

    pr(X=x)=b(x;p,n)=\dfrac{n!}{x!(n-x)!}p^x(1-p)^{n-x};\ \ \ \ n=4, p=0.5; x=0,1,..4

    CB
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