From Osher Doctorow
The power pdf fX(x) is:
1) fX(x) = ab^a x^(a - 1), a and b > 0, x on [0, 1/b]
Let's take b = 1 for simplicity. Then:
2) fX(x) = ax^(a - 1), x on [0, 1]
Setting this equal to 1/2 results in:
3) ax^(a - 1) = 1/2
so the solution is given by:
4) x^(a - 1) = 1/(2a)
5) x = (1/(2a))^(1/(a-1))
By l'Hospital's rule, as a --> infinity, x --> 1 since log(x) --> 0.
Osher Doctorow
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