# Bounded Versus Unbounded A Probability Distribution

Bounded Versus Unbounded A probability Distribution is bounded if there are values A and B such that no possible value can be less than A or greater than B. The value A is then the minimum possible value, and the value B is the maximum possible value. The distribution is unbounded if there are no such bounds. Of course, it is possible for a distribution to be bounded in one direction but not the other. As an example, the distribution of scores on a 100-point exam is bounded between 0 and 100. In contrast, the distribution of the amount of damages Mr. Jones submits to his insurance company in a year is bounded on the left by 0, but there is no natural upper bound. Therefore, you might model this amount with a distribution that is bounded by 0 on the left but is unbounded on the right. Alternatively, if you believe that no damage amount larger than \$20,000 can occur, you could model this amount with a distribution that is bounded in both directions.

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