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 !

$Pr(U = b) = Pr(Y \geq b) = \int_{b} ^{\infty} f_Y(y) dy$
$f_U(u) = f_Y(u)$ for $u < b$ 
Hence, the CDF of $u$ will be , 
$F_U(u) = F_Y(u)$ for $u < b$
$F_U(u) = 1 $ for $u \geq b$ as $F_U(b) = F_Y(b) + Pr(U = b) = 1 $, and it will stay at $1$. 
The best way to explain this is that $F_U(u_0)$ is the probability that $u \leq u_0$. So, as the variable $u$ is truncated at $b$, so it will be always less than $b$ and any value greater than $b$. 
