Which of the following functions provides the likelihood of each possible value of a discrete random variable?

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Which of the following functions provides the likelihood of each possible value of a discrete random variable?

The probability mass function (PMF) is the function that provides the likelihood of each possible value of a discrete random variable. It assigns a probability to each discrete outcome, allowing us to understand how probabilities are distributed across the possible values the random variable can take. For a discrete random variable, the PMF must satisfy two key properties: the sum of all probabilities must equal one, and each individual probability must be non-negative. Therefore, if you have a random variable that can take specific values, the PMF gives you the likelihood—the fundamental aspect of probability—of observing each of those values. In contrast, the cumulative distribution function (CDF) provides the probability that the random variable will take a value less than or equal to a particular point, which is a cumulative measure rather than an individual likelihood. The density function, often used in the context of continuous random variables, addresses probability density rather than distinct probabilities. Lastly, the variance function relates to the measure of dispersion of the random variable rather than its probability distribution.

The probability mass function (PMF) is the function that provides the likelihood of each possible value of a discrete random variable. It assigns a probability to each discrete outcome, allowing us to understand how probabilities are distributed across the possible values the random variable can take.

For a discrete random variable, the PMF must satisfy two key properties: the sum of all probabilities must equal one, and each individual probability must be non-negative. Therefore, if you have a random variable that can take specific values, the PMF gives you the likelihood—the fundamental aspect of probability—of observing each of those values.

In contrast, the cumulative distribution function (CDF) provides the probability that the random variable will take a value less than or equal to a particular point, which is a cumulative measure rather than an individual likelihood. The density function, often used in the context of continuous random variables, addresses probability density rather than distinct probabilities. Lastly, the variance function relates to the measure of dispersion of the random variable rather than its probability distribution.

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