How can the CDF for a discrete random variable be obtained?

How can the CDF for a discrete random variable be obtained?

• A. By calculating the mean of the PMF
• B. By summing the probabilities of the PMF up to a certain value
• C. By multiplying the PMF by a constant factor
• D. By integrating the PMF across the entire space

Answer: (B)

The cumulative distribution function (CDF) for a discrete random variable can be obtained by summing the probabilities from the probability mass function (PMF) for values up to a specified point. The CDF at a value x gives the probability that the random variable is less than or equal to x. To derive the CDF, you start with the PMF, which provides the probabilities for each possible value that the random variable can take. By accumulating (or summing) these probabilities from the lowest value up to the value x, you calculate the total probability that the random variable is less than or equal to x. This process is fundamental in probability theory, as it constructs the CDF step by step, capturing the entire distribution of the random variable. This method highlights the nature of discrete random variables, where specific probabilities are assigned to distinct outcomes, allowing for cumulative probabilities to be easily calculated through addition.

The cumulative distribution function (CDF) for a discrete random variable can be obtained by summing the probabilities from the probability mass function (PMF) for values up to a specified point. The CDF at a value x gives the probability that the random variable is less than or equal to x.

To derive the CDF, you start with the PMF, which provides the probabilities for each possible value that the random variable can take. By accumulating (or summing) these probabilities from the lowest value up to the value x, you calculate the total probability that the random variable is less than or equal to x. This process is fundamental in probability theory, as it constructs the CDF step by step, capturing the entire distribution of the random variable.

This method highlights the nature of discrete random variables, where specific probabilities are assigned to distinct outcomes, allowing for cumulative probabilities to be easily calculated through addition.