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

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

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

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onyebuchinnaji onyebuchinnaji · Answer 2 · 2022-04-15T08:37:17-04:00

The probability of numbers within (13 x 15) to be found in numbers within (8 x 12) inclusively, is zero.

Boundary of the function

The boundary of the distributed function of x is between 8 and 12 inlcusive, which is written as follows;

8 ≤ x ≤ 12

Elements within the boundary of 8 ≤ x ≤ 12, = {8, 9, 10, 11, 12}

Elements within the boundary of 13 ≤ x ≤ 15, = {13, 14, 15}

The common elements = 0
Probability = 0

Thus, the probability of numbers within (13 x 15) to be found in numbers within (8 x 12) inclusively, is zero.

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