Which function describes the distribution of probabilities for discrete random variables?

Which function describes the distribution of probabilities for discrete random variables?

• A. Cumulative Distribution Function
• B. Moment Generating Function
• C. Probability Mass Function
• D. Probability Density Function

Answer: (C)

For a discrete random variable, the distribution of probabilities is captured by the probability mass function. The PMF assigns a probability to each possible value x, written as P(X = x), and the sum of these probabilities over all possible values equals 1. This directly describes how likely each outcome is. The cumulative distribution function, while related, gives P(X ≤ x) and describes accumulated probability rather than the exact probability of each value. The probability density function is used for continuous variables and does not assign probabilities to individual outcomes in the same way. The moment generating function encodes moments like the mean and variance, not the actual probabilities. So the probability mass function is the appropriate descriptor for discrete distributions.

For a discrete random variable, the distribution of probabilities is captured by the probability mass function. The PMF assigns a probability to each possible value x, written as P(X = x), and the sum of these probabilities over all possible values equals 1. This directly describes how likely each outcome is. The cumulative distribution function, while related, gives P(X ≤ x) and describes accumulated probability rather than the exact probability of each value. The probability density function is used for continuous variables and does not assign probabilities to individual outcomes in the same way. The moment generating function encodes moments like the mean and variance, not the actual probabilities. So the probability mass function is the appropriate descriptor for discrete distributions.