Final answer:
Lower(X) refers to the probability of a random variable X being less than or equal to a certain value 'x', which is represented as the Cumulative Distribution Function (CDF).
Step-by-step explanation:
The term Lower(X) in the context of probability refers to the value of a random variable X being less than or equal to a particular value x. When you see Lower(X), it is asking for the probability that the random variable X is less than or equal to a value 'x', known as the Cumulative Distribution Function (CDF). In the case of continuous distributions, this probability is represented as P(X ≤ x), which provides the area to the left of x on the probability distribution graph.
To calculate the probability of a random variable being greater than a certain value, which is denoted as P(X > x), you would use the formula P(X > x) = 1 − P(X < x) for continuous distributions. This subtracts the probability of X being less than or equal to x from 1, effectively giving the area to the right on the probability distribution graph.