PMF and CDF Calculator

Probability Mass Function (PMF) and Cumulative Distribution Function (CDF) Graphing Calculator

Posted by Krystian Wojcicki on Friday, October 30, 2020 Tags: Calculator   4 minute read


Probability Mass Function (PMF)

$$ x $$
$$ p(x) $$

Cumulative Distribution Function (CDF)

PMF and CDF Explanations


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 \(p_X(x_i) \geq 0\).


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 \(\leq x\).