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If the random variable x has a uniform distribution between 40 and 50, then p(35 ≤ x ≤ 45) is:

User Bluu
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\mathbb P(35\le X\le45)=\mathbb P(X\le45)-\mathbb P(X\le35)=F_X(45)-F_X(35)

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


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

which yields the CDF


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

and so


\mathbb P(35\le X\le45)=(45-40)/(10)-0=\frac12
User Keena
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