Consider the two cases (a) D OE0;1OE , .!/ D e!, X.!/ D .!=/1= for ! 2 and ; > 0, (b) D =2;

Consider the two cases

(a) D OE0;1OE , .!/ D e!, X.!/ D .!=˛/1=ˇ for ! 2 and ˛; ˇ > 0,

(b) D

=2; =2OE , .!/ D 1=, X.!/ D sin2 ! for ! 2 .

In each case, show that is a probability density and X a random variable on . ;B/, and calculate the distribution density of X with respect to the probability measure P with density . (The distribution of X in case

(a) is called the Weibull distribution with parameters

˛; ˇ, in case

(b) the arcsine distribution.)