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• The probability mass function (pmf) characterizes the distribution of a discrete random variable.
• Often, probability mass functions are plotted as column charts.
• The probability mass function above is defined in the “standardized” form.
• We can add the corresponding values from the pmf.
• Plug each value of \(x\) into the pmf.
• The Symbulate pmf method can be used to compute the pmf for named distributions.
• The constant \(e^{-2.3}\) doesn’t affect the shape of the probability mass function.
• Plot the probability mass functions for the Poisson distribution with mean 4.5 and 12 respectively.
• …distribution is defined by a probability mass function, denoted by f(x).
• The probability mass function of a discrete random variable is a list of probabilities associated with each of its possible values.
• The Probability Mass function is defined on all the values of R, where it takes all the argument of any real number.
• This is the reason why probability mass function is used in computer programming and statistical modelling.
• Probability mass function plays an important role in statistics.
• We can represent probability mass functions numerically with a table, graphically with a histogram, or analytically with a formula.
• In the next three sections, we will see examples of pmf's defined analytically with a formula.
• A probability mass function (PMF)— also called a frequency function— gives you probabilities for discrete random variables .
• The area under a graph of a probability mass function is 100% (i.e. the probability of all events, when added together, is 100%).
• However, some authors (not many) use the term “probability mass function” to mean either a discrete or continuous probability distribution.
• The aim of the probability mass function is to describe the probability of each possible value.
• We also have two probability mass functions associated with the random variables: P(x) and P(y).
• In the case of the probability mass function, we saw that the y-axis gives a probability.
• An example of a multivariate discrete distribution , and of its probability mass function, is provided by the multinomial distribution .
• The binomial probability mass function is a very common discrete probability mass function that has been studied since the 17th century.
• Figure 1 shows this probability mass function for the case p = 0 .

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