The P(X ≤ x) is an example of a cumulative probability.Group of answer choicesTrueFalse

Final Answer

True

Explanation

In probability theory, $P(X ≤ x)$ represents the cumulative distribution function (CDF) of a random variable $X$. The CDF gives the probability that the variable $X$ will take a value less than or equal to $x$. This is a fundamental concept in statistics and probability because it helps describe the distribution of a random variable.

The CDF is always a non-decreasing function and ranges from 0 to 1, where:

• $P(X ≤ x) = 0$ for $x$ values that are less than the minimum value of $X$.
• $P(X ≤ x) = 1$ for $x$ values that are equal to or greater than the maximum value of $X$.

This definition makes it clear that $P(X ≤ x)$ is indeed an example of a cumulative probability, as it accumulates the probabilities of all outcomes up to a certain threshold $x$. Given this definition and explanation, the statement is confirmed to be true.