It appears that there might be some confusion in your statement. Let me clarify a few concepts related to probability distributions, cumulative distribution functions (CDF), and medians.
Probability Distribution Function (PDF): The probability distribution function (PDF) of a random variable X provides the probability of observing a specific value or falling within a specific range. The PDF is usually denoted as f(x), and it's used for continuous random variables. The integral of the PDF over a range gives the probability of X falling within that range.
Cumulative Distribution Function (CDF): The cumulative distribution function (CDF), denoted as F(x), provides the probability that the random variable X takes on a value less than or equal to x. In mathematical terms, F(x) = P(X ≤ x). The CDF is defined for both continuous and discrete random variables.
Median: The median of a probability distribution is a value that separates the distribution into two equal areas, such that 50% of the probability mass is on one side, and 50% is on the other side. For a continuous random variable, the median is the value x for which F(x) = 0.5, or P(X ≤ x) = 0.5.
However, in your statement, you mentioned "F(x) = 0, 5." This doesn't represent a proper cumulative distribution function (CDF), as CDFs should take values between 0 and 1. If you meant that the median is the value of x for which F(x) = 0.5, that would be correct.
If you have a specific probability distribution or CDF that you'd like assistance with, please provide more details, and I'll be happy to help.