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Math Help - Median of a two uniform distributions added together

  1. #1
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    Median of a two uniform distributions added together

    Hello all,

    I am trying to find the general way of finding the median of two continuous uniform distributions. Lets say I am trying to find the median height for all high school students in my town, and there are two high schools. The heights in high school 1 are uniformly distributed between a and b (so the median height in high school 1 is (a+b) / 2. The heights in high school 2 are uniformly distributed between 0 and b (so the median height in high school b is b/2).

    To make things complicated, suppose high school 1 is x times larger than high school 2. Is there a general way of finding the median height of high schoolers in this case? Please let me know if these needs clarification and any help is greatly appreciated,

    Cheers,

    Nick
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  2. #2
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    Re: Median of a two uniform distributions added together

    Are the two distributions independent?
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  3. #3
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    Re: Median of a two uniform distributions added together

    Yes, a random draw at high school 1 will not affect the draw at high school 2
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