What does the probability function provide for a discrete random variable?

The probability function for a discrete random variable is designed to specify the likelihood of that variable taking on specific values. When we refer to the probability function, we are typically discussing the probability mass function (PMF), which assigns probabilities to each possible value of the discrete random variable. This function tells us how likely it is for the variable to equal a particular value.

For example, if we have a discrete random variable representing the roll of a die, the probability function would indicate that the probability of rolling a 3 is ( \frac{1}{6} ), while the probabilities of rolling each of the other numbers (1, 2, 4, 5, and 6) would similarly be ( \frac{1}{6} ). Thus, the correct choice identifies the fundamental purpose of the probability function, which is to determine the probability of the variable assuming specific values.

The other choices refer to different statistical concepts. The mean and variance are measures that summarize properties of the probability distribution, but they do not represent the function itself. The mean describes the average expected outcome, while the variance indicates the degree of variability around that mean. The distribution of values could refer to the overall shape or characteristics of the probability function, but it