Suppose $X$ and $U$ are independent random variables. $X$ is the discrete uniform distribution and $U$ is the continuous uniform distribution from $[0,1]$. What is the $P(X+Y\leq y)$, where $y$ is a real number?

Suppose $X$ and $U$ are independent random variables. $X$ is a discrete uniform variable and $U$ is a continuous uniform $[0,1]$ variable. What is the value of $\mathbb P(X+U\leq y)$, where $y$ is a real number?

Suppose X and U are independent random variables. X is the discrete uniform distribution and U is the continuous uniform distribution from [0,1]. What is the P(X+Y<=y), where y is a real number?

Suppose $X$ and $U$ are independent random variables. $X$ is the discrete uniform distribution and $U$ is the continuous uniform distribution from $[0,1]$. What is the $P(X+Y\leq y)$, where $y$ is a real number?