6.2 Suppose X follows a continuous uniform distribution from 1 to 5. Determine the conditional probability P(X > 2.5 | X ≤ 4).

The problem is asking for the conditional probability that X is greater than 2.5 given that X is less than or equal to 4.

Step 1: Identify the range of the uniform distribution. In this case, it's from 1 to 5.

Step 2: Identify the range of the conditional event. In this case, it's from 1 to 4.

Step 3: Identify the range of the event of interest. In this case, it's from 2.5 to 4.

Step 4: Calculate the length of the range of the conditional event. This is 4 - 1 = 3.

Step 5: Calculate the length of the range of the event of interest. This is 4 - 2.5 = 1.5.

Step 6: The conditional probability is the ratio of the length of the range of the event of interest to the length of the range of the conditional event. So, P(X > 2.5 | X ≤ 4) = 1.5 / 3 = 0.5.

So, the conditional probability P(X > 2.5 | X ≤ 4) is 0.5.