The probability mass function (PMF) describes which aspect of a discrete random variable?

The probability mass function (PMF) describes which aspect of a discrete random variable?

• A. The cumulative probability across all outcomes
• B. The individual probabilities of each outcome
• C. The average result of trials performed
• D. The expected value calculated from a subset

Answer: (B)

The probability mass function (PMF) is specifically designed to quantify the individual probabilities associated with each possible outcome of a discrete random variable. In essence, it assigns a probability value to each outcome, ensuring that these probabilities are non-negative and sum up to one across all possible outcomes in the sample space. For a discrete random variable, the PMF provides a complete probability distribution that allows us to understand how likely each outcome is. For instance, if you have a dice roll represented as a discrete random variable, the PMF would indicate that the probability of rolling a 1, 2, 3, 4, 5, or 6 is equal to \( \frac{1}{6} \) for each face of the die. This understanding contrasts with other options: the cumulative probability function would describe the probability that the random variable takes on a value less than or equal to a certain number (not individual probabilities), while the average result of trials pertains to the concept of expected value, which involves aggregating outcomes and their probabilities rather than focusing on individual probabilities as the PMF does. Furthermore, the expected value calculated from a subset relates to the average outcome from a selection of values rather than the distribution of probabilities themselves. Thus, choosing

The probability mass function (PMF) is specifically designed to quantify the individual probabilities associated with each possible outcome of a discrete random variable. In essence, it assigns a probability value to each outcome, ensuring that these probabilities are non-negative and sum up to one across all possible outcomes in the sample space.

For a discrete random variable, the PMF provides a complete probability distribution that allows us to understand how likely each outcome is. For instance, if you have a dice roll represented as a discrete random variable, the PMF would indicate that the probability of rolling a 1, 2, 3, 4, 5, or 6 is equal to ( \frac{1}{6} ) for each face of the die.

This understanding contrasts with other options: the cumulative probability function would describe the probability that the random variable takes on a value less than or equal to a certain number (not individual probabilities), while the average result of trials pertains to the concept of expected value, which involves aggregating outcomes and their probabilities rather than focusing on individual probabilities as the PMF does. Furthermore, the expected value calculated from a subset relates to the average outcome from a selection of values rather than the distribution of probabilities themselves. Thus, choosing