Probability Histogram

A probability histogram simply displays in graphical form the nature of a probability distribution.

The construction is very straight-forward. For example, given the following probability distribution:

$$\begin{array}{c|c|c|c|c|c}X & 0 & 1 & 2 & 3 & 4\\ \hline P(X) & 0.1 & 0.2 & 0.4 & 0.2 & 0.1\\\end{array}$$

The probability histogram would look like

where each bar's height is determined by the magnitude of the probability associated with the outcome that bar represents.

Note where the boundaries between the bars are located (on the ".5"'s, in this case). This becomes an important consideration in the "continuity correction" for a Normal Distribution approximation to a Binomial Distribution probability.