For what values of the parameters are the following functions probability density functions? (a) f(x) = C{x(1 x)}-1/2, 0

For what values of the parameters are the following functions probability density functions? (a) f(x) = C{x(1 x)}-1/2, 0 < x="">< 1, the density function of the 'arc sine law'. (b) f(x) = c exp( x e—x), x e r, the density function of the 'extreme-value distribution'. (c) fix) = c(1 ± x2)-' 7 2, x e r. 1,="" the="" density="" function="" of="" the="" 'arc="" sine="" law'.="" (b)="" f(x)="C" exp(="" x="" e—x),="" x="" e="" r,="" the="" density="" function="" of="" the="" 'extreme-value="" distribution'.="" (c)="" fix)="C(1" ±="" x2)-'="" 7="" 2,="" x="" e="">