Here is my Problem.
Let X~Uniform(0,2) and Y~Normal(0,1) be independent random variables. Let
Z ={1 if X > Y
{2 if X <Y
Find E[Z] and V ar[Z]. You may leave your answers in terms of denite integrals.
My big question is, how can we join a uniform and a normal distribution on the same probability density function.
Thank you
Some cautions have to be taken because X and Y are continuos variables and Z is a discrete variable. The most sure way is to valuate the probability...
(1)
The first step...
(2)
(3)
Now other steps are...
a) use (2) and (3) to obtain (1)...
b) compute the derivative of (1) respect to ...
c) compute...
(4)
d) use the result c) to compute , , ...
All these steps are left to You...
Kind regards