On Independence and Dependence Properties of a Set of Random Events

Abstract

For a set of random events, we introduce the notions of independence, partial independence, dependence, and total dependence at a given level. For illustration purposes, we present four examples. In Example 1, two sets of totally dependent events are constructed. In Example 2, the existence of partially independent events at all levels, except at the highest one, is demonstrated. In Example 3, we exhibit a case in which the events are independent at higher levels but are totally dependent at lower levels. In Example 4, we have n events satisfying all the conditions needed to be mutually independent, except one.

Key Words:

• Dependence
• Independence
• Random events