Assuming \(f(x)\) is the PMF and \(F(x)\) refers to the CDF, and provided that \(x\in\{1,2,3\}\) (as in your previous question), you have
\(F(x)=\begin{cases}0&\text{for }x<1\\\\\dfrac{25}{31}&\text{for }1\le x<2\\\\\dfrac{30}{31}&\text{for }2\le x<3\\\\1&\text{for }x\ge3\end{cases}\)
This comes from the definition of the CDF:
\(F(x)=\mathbb P(X\le x)=\sum_i\mathbb P(X=i)\)
Now,
\(F(1)=\dfrac{25}{31}\)
\(F(2)=\dfrac{30}{31}\)
\(\mathbb P(X\le1.5)=F(1.5)=\dfrac{25}{31}\)
\(\mathbb P(X>2)=1-\mathbb P(X\le2)=1-F(2)=1-\dfrac{30}{31}=\dfrac1{31}\)
\(\mathbb P(1
