Distribution function

X 2 3 4
P 0.35 0.35 0.3

The data in this table do I calculate the distribution function F(x) and then probability p(2.5 < ξ < 3.25) p(2.8 < ξ) and p(3.25 > ξ)

Correct result:

p₁ =  0.35
p₂ =  0.3
p₃ =  0.65

Solution:

$$\begin{gathered} F_2=0.3 \\ {F}_3=F_2+0.35=0.3+0.35={\displaystyle \frac{13}{20}}=0.65 \\ {F}_4=F_3+0.35=0.65+0.35=1 \\ {p}_1=0.35={\displaystyle \frac{7}{20}} \end{gathered}$$

$p_2=0.3={\displaystyle \frac{3}{10}}$

$p_3=0.3+0.35={\displaystyle \frac{13}{20}}=0.65$

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