Are the two distributions independent?
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,