Final answer:
The student's question concerns a discrete probability distribution of a variable x that can take two values with associated probabilities p and 1-p, adhering to the properties of probability distributions.
Step-by-step explanation:
The question relates to probability distribution functions (PDFs), specifically concerning a discrete distribution where a variable x can take on only two values, 1 and -1. The probabilities associated with these values are p for x=1 and 1-p for x=-1. These probabilities must meet two conditions: they must each be between zero and one, inclusive, and their sum must be equal to one. This is in accordance with the fundamental properties of probability distributions.
To analyze such distributions, we might use concepts like the cumulative distribution function (CDF) for continuous distributions, which is used to determine the probability that the variable is less than or equal to a particular value (noted as P(X <= x)).
Conversely, P(X > x) for a continuous distribution can be determined by subtracting the CDF from one. However, in the case of discrete distributions, such as the one presented in the question, we would use the discrete probabilities directly without the need for integrating a PDF.