Question

Suppose that f(x) = x/8 for 3 < x < 5. Determine the following probabilities:

a. P(X < 4)
b. P(X > 3.5)
c. P(4 < X < 5)
d. P(X < 4.5)
e. P(X < 3.5 or X > 4.5)

Answer 1

The probabilities asked to be computed in the question relate to the function f(x) = x/8 in a specific range and need the complete probability distribution function and potentially its cumulative distribution function, which have not been provided in the question.

Step-by-step explanation:

The question asks us to determine the probabilities related to a function f(x) = x/8 for a continuous range between 3 and 5. The probabilities for events such as P(X < 4), P(X > 3.5), etc., are to be calculated as areas under the curve of the probability distribution function.

For a continuous distribution, certain probabilities can be determined using the Cumulative Distribution Function (CDF), which only provides probabilities for x less than a certain value. Therefore, to calculate probabilities like P(X < 4) or P(4 < X < 5), we would integrate the probability density function (PDF) over the desired range.

However, we cannot calculate these probabilities directly from the provided snippets since the problem seems to relate to a specific PDF and potentially a CDF associated with it, neither of which is fully provided. Thus, please provide the complete function or the necessary details associated with it so we can accurately compute the probabilities.