Below is the distribution function:
What does etc mean? Are they like some sort of indicator function? For example in this case, when x= 1/2, it's 0 and when x=3/2, it's 1.
P(X=0)=.25
P(X=1)=.5
P(X=2)=.25
You can see the jumps at those point, which are the probabilities.
That is a sum of indicator functions that achieves one after 2.
Both of you comments are wrong.
At 1/2, only the first indicator is 1, hence F(.5)=1/4
At 3/2, the first two indicators are 1, hence F(1.5)=1/4+1/2=3/4.
Finally at 2 or afterwards F(x)=1/4+1/2+1/4=1