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Math Help - median of a sampling distribution

  1. #1
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    median of a sampling distribution

    hi i'm a bit confused on a simple question which i thought i did correct, but the mark scheme has a different answer.

    A bag contains a large number of coins:
    75% are 10p coins,
    25% are 5p coins.

    A random sample of 3 coins is drawn from the bag.
    Find the sampling distribution for the median of the values of the 3 selected coin
    s

    and the answer is:

    Median 5: p = (0.25)^3 + 3(0.75)(0.25)^2 = 10/64

    Median 10: p = (0.75)^3 + 3(0.25)(0.75)^2 = 54/64

    so basically they are using the case for median 5 with 2 5's or 3 5's, but these are the combinations:

    Median 5: (5 5 5) (5 5 10) (10 5 10) (10 5 5)

    Median 10: (10 10 10) (5 10 10) (10 10 5) (5 10 5)

    why are the combinations i've shown in red used the other way around?
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  2. #2
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    Quote Originally Posted by Aquafina View Post
    hi i'm a bit confused on a simple question which i thought i did correct, but the mark scheme has a different answer.

    A bag contains a large number of coins:
    75% are 10p coins,
    25% are 5p coins.

    A random sample of 3 coins is drawn from the bag.
    Find the sampling distribution for the median of the values of the 3 selected coin
    s

    and the answer is:

    Median 5: p = (0.25)^3 + 3(0.75)(0.25)^2 = 10/64

    Median 10: p = (0.75)^3 + 3(0.25)(0.75)^2 = 54/64
    median(med) is discrete rv. It takes the values 5 and 10.
    we have
     p\{med =5\}=
    P{ we draw two coins 5p, one coin 10p}+P{we draw all of coins 5p}
     C_3^2(0.25)^2 (0.75) +(0.25)^3
    (because three drawing coins are independent)
    similar, we get p{med =10}
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  3. #3
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    Quote Originally Posted by Aquafina View Post
    Median 5: (5 5 5) (5 5 10) (10 5 10) (10 5 5)

    Median 10: (10 10 10) (5 10 10) (10 10 5) (5 10 5)

    why are the combinations i've shown in red used the other way around?
    the combination (10 5 10) have median 10. For getting the median, the first step we have to order from low to higher. The combination (5, 10 5) have median 5.
    Median - Wikipedia, the free encyclopedia
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  4. #4
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    thanks! seems like a stupid question now, but the ordering didn't hit me then.

    Thanks
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