Determine the Cumulative Distributive Distribution(CDF) of a truncated value? 
It is the last part(part h) that I am having problems with. 
I know you use integration and then split it into 2 parts. 
But how exactly do you do it ? A detailed answer would be very helpful ! 
Please help !

It is a lot simpler than you might think.  Here is a hint:  there are two cases if $U = \min\{Y, b\}$.  Either $Y < b$ or $Y \ge b$.  If the latter, then $\Pr[U = b] = \Pr[Y \ge b] = S_Y(b)$.  Otherwise, $Y < b$ implies $U = Y$ and you already know the density for that situation.
