For discrete random variables, what is the name of the probability formula?

For discrete random variables, what is the name of the probability formula?

• A. Probability density function
• B. Probability mass function
• C. Cumulative distribution function
• D. Moment generating function

Answer: (B)

The probability mass function describes the probabilities for discrete outcomes. For a discrete random variable X, it assigns a value p(x) = P(X = x) to each possible outcome x. The probabilities must sum to 1 across all possible x. For example, if X represents the roll of a fair die, X can take values 1 through 6 and p(x) = 1/6 for each x in {1,2,3,4,5,6}. This is different from the probability density function, which is used for continuous variables and is not interpreted as a probability at a single point (probabilities come from integrating the density over an interval). The cumulative distribution function F(x) = P(X ≤ x) is another description that applies to both discrete and continuous cases, but it gives the probability up to x, not the probability of a single value. The moment generating function M_X(t) = E[e^{tX}] relates to moments of the distribution, not to the probability of specific outcomes.

The probability mass function describes the probabilities for discrete outcomes. For a discrete random variable X, it assigns a value p(x) = P(X = x) to each possible outcome x. The probabilities must sum to 1 across all possible x. For example, if X represents the roll of a fair die, X can take values 1 through 6 and p(x) = 1/6 for each x in {1,2,3,4,5,6}. This is different from the probability density function, which is used for continuous variables and is not interpreted as a probability at a single point (probabilities come from integrating the density over an interval). The cumulative distribution function F(x) = P(X ≤ x) is another description that applies to both discrete and continuous cases, but it gives the probability up to x, not the probability of a single value. The moment generating function M_X(t) = E[e^{tX}] relates to moments of the distribution, not to the probability of specific outcomes.