Respuesta :

LammettHash
Assuming [tex]f(x)[/tex] is the PMF and [tex]F(x)[/tex] refers to the CDF, and provided that [tex]x\in\{1,2,3\}[/tex] (as in your previous question), you have

[tex]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}[/tex]

This comes from the definition of the CDF:

[tex]F(x)=\mathbb P(X\le x)=\sum_i\mathbb P(X=i)[/tex]

Now,

[tex]F(1)=\dfrac{25}{31}[/tex]
[tex]F(2)=\dfrac{30}{31}[/tex]
[tex]\mathbb P(X\le1.5)=F(1.5)=\dfrac{25}{31}[/tex]
[tex]\mathbb P(X>2)=1-\mathbb P(X\le2)=1-F(2)=1-\dfrac{30}{31}=\dfrac1{31}[/tex]
[tex]\mathbb P(1<X\le2)=\mathbb P(X=2)=f(2)=\dfrac5{31}[/tex]

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