For tossing three coin find the C.D.F

S={HHH,HTH,HHT,THH,HTT,THT,TTH,TTT}
If  X<0  ,then F(x)=0
If  0≤X<1  ,then F(x)=F(0)=1/8
If  1≤X<2  ,then F(x)=F(1)=P(X≤1)=P(0)+P(1)=1/8+3/8=4/8=1/2
If  2≤X<3  ,then F(x)=F(2)=P(X≤2)=P(0)+P(1)+P(2)=1/2+3/8=7/8
If 3≤X  ,then F(x)=F(3)=P(X≤3)=P(0)+P(1)+P(2)+P(3)=1
Thus, the C.D.F can be expressed as:
F(x)={(   0       X<0        1/8      0≤X<1       1/2       1≤X<2             7/8          2≤X<3  1        3≤X)┤