Question

If x is uniformly distributed over the interval 8 to 12, inclusively (8 x 12), then the probability, p(13 x 15), is ____________ .

Answer 1

$f_X(x)=\begin{cases}\dfrac1{12-8}=\dfrac14&\text{for }8\le x\le12\\\\0&\text{elsewhere}\end{cases}$

This means $\mathbb P(13\le x\le15)=0$ since this interval lies outside the support of the density function.