Find pmf of the function $Y(t)=rect(t-.5-D)$ where $D$ is uniform over (0,1)

Question

The random process with $Y(t)=rect(t-.5-D)$ where $D$ is uniform over (0,1) Find its probability mass function.What do I with the uniform stuff in the rect function?

So $f_D(d)=d$ for $0<d<1$ and 0 elsewhere. So the pmf should be: $f_{Y(t)}y(t)=rect(t-.5-d)$ for $0<d<1$ and 0 elsewhere. Does it look right?