What are the possible values of the product of two indicator random variables, IA and IB, associated with events a and b, with nonempty intersections?
To determine the possible values of the product of two indicator random variables, IA and IB, associated with events a and b, with nonempty intersections, we need to consider the definitions of indicator random variables and their properties.
Indicator random variables are binary random variables that take the value 1 if a specific event occurs and 0 otherwise. In this case, IA takes the value 1 when event a occurs and 0 otherwise, while IB takes the value 1 when event b occurs and 0 otherwise.
Since IA and IB are indicator random variables, their possible values are restricted to either 0 or 1. Therefore, the product of IA and IB can only take the values 0 or 1.
If the intersection of events a and b is nonempty, it means that there are outcomes for which both events occur simultaneously. In this case, the product IA * IB will be 1, indicating that both IA and IB are equal to 1.
In summary, the possible values of the product of two indicator random variables, IA and IB, associated with events a and b, with nonempty intersections, are restricted to 0 or 1, with the value 1 occurring when both events occur simultaneously.