# 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

# Calculator

## Probability Mass Function (PMF)

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

# 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 $$\leq x$$.