hi there,

Given two independent stochastic variables X and Y. X is exponentially distributed with parameter a and Y is exponentially distributed with parameter b. We define two new stochastic variables T and Z by:

(T, Z):= (X, 0) if X <= Y
(T, Z):= (Y, 1) if X > Y

How can I determine the distributions of T and Z and show that T and Z are independent?
I would really appreciate some help!

Kind regards
Joolz