Consider two independent random variables: X~U(0,1) and Y~U(0,2). Let Z = min(X,Y).
b) Find F$_Z$(z) in terms of F$_X$(.) and F$_Y$(.).
c) Eliminate F$_X$(.) and F$_Y$(.) to find F$_Z$(z).
What is the difference between these two questions when (from what I can tell) they're both finding the cumulative distribution function of the same thing? What does it mean by eliminate?
Our lecture notes don't contain any examples and I can't find anything on Google. Can anyone please demonstrate how to solve these seemingly identical(?) questions?
I can find the c.d.f of Z by finding 1 - F$_Z$ using P(Z > z), but I'm not sure which question this method falls under. I'm not even sure if there is another method.
Thanks