Re: Min of two Uniformly distributed random variables

Hello, I have a problem of determining the
distribution of a min
function.

a,b,c are positive real numbers where 0<a-b<c

X is a uniformly distributed random variable U(a-c,b)

Y=min{a+b-2X, 2X+2c-a-b)

When I simulate it, I see that Y has a triangular
shape. But I need to
formally prove it.

Any idea?

Thanks.




Use the fact that

Y = a+b-2X if X >= (a+b-c)/2
Y = 2X+2c-a-b if X <=(a+b-c)/2

and X is uniform.

Jack
.