Suppose x follows a continuous uniform distribution from 1 to 5. determine the conditional probability p (x >2.5 | x ≤ 4).

Because the random variable x follows a continuous uniform distribution from x=1 to x=5, therefore

p (x) = 1/4, x=[1, 5]

The value of p (x) ensures that the total area under the curve = 1.

The conditional probability p (x > 2.5 | x ≤ 4) is the shaded portion of the curve. Its value is

p (x > 2.5 | x ≤4) = (1/4) * (4 - 2.5) = 0.375

Answer: 0.375