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Probability Mass Function (PMF)
| $$ x $$ | ||||
| $$ p(x) $$ |
Cumulative Distribution Function (CDF)
PMF and CDF Explanations
PMF
The PMF of a random variable \(X\) is a function associating the possible values of \(X\) and their associated probabilities; for example \(p_{X}(x_i) = P(X = x_i)\). A PMF can be created by filling in a table, one row representing all possible values, while the other row represents the associated probabilities. One has to ensure that \(\sum_{x_i \in X} p_X(x_i) = 1\) and that \(p_X(x_i) \geq 0\).
CDF
The CDF of a random variable \(X\) is a function that represents the probability that \(X\) will be less than or equal to \(x\). The function is defined as \(F_X(x) = P(X \leq x)\). Using the table generated while creating the PMF one can calculate the value of \(F_X(x)\) by summing all associated probabilities for possible values \(\leq x\).
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