Respuesta :

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[tex]\mathbb P(35\le X\le45)=\mathbb P(X\le45)-\mathbb P(X\le35)=F_X(45)-F_X(35)[/tex]

where [tex]F_X(x)[/tex] is the cumulative distribution function of [tex]X[/tex]. We have probability density given by

[tex]f_X(x)=\begin{cases}\frac1{10}&\text{for }40\le x\le50\\\\0&\text{otherwise}\end{cases}[/tex]

which yields the CDF

[tex]F_X(x)=\begin{cases}0&\text{for }x<40\\\\\frac{x-40}{10}&\text{for }40\le x<50\\\\1&\text{for }x\ge50\end{cases}[/tex]

and so

[tex]\mathbb P(35\le X\le45)=\dfrac{45-40}{10}-0=\dfrac12[/tex]

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