$U$ is a random variable in the range of $(0,3)$. The random variable $W$ is the output of the clipper described by
$W=g(U)=U$ for $U\le 1$ and $1$ for $U>1$
find the cdf of $FW(w)$
Any ideas on how to solve this?
My idea was to graph it $g(U)$ vs $U$ and then see that the integral of the CDF is just area under the curve. However I think I am doing something wrong with my plot as I am getting the CDF$>1$?
If $U$ is a uniformly distributed random variable, then its density function equals $1/3$ on the given interval. Also, $W$ has a range from zero to 1 (even though its domain is the range of $U$. For all values of $w$ between 0 and 1, the probability density is $1/3$, and for 1, it's $2/3$.
So,
$$ F_W(w) = \begin{cases} 0, & w \le 0, \\ w/3, & 0 \lt w < 1, \\ 1, & w \ge 1 \end{cases} $$
Note the discontinuity.