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Suppose that X and Y are indicators of A and B respectively. Show that 1−X,max(X,Y),XY are...

Suppose that X and Y are indicators of A and B respectively. Show that 1−X,max(X,Y),XY are all indicators and identify the corresponding events in terms of A and B.

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Answer #1

Let X and Y be indicators of A and B

That is , if event A has occurred, then X=1 and X=0 otherwise.

Similarly, if event B has occurred, then Y=1 and Y=0 otherwise.

1-X is an indicator function of A' (compliment of A). Here, if event A has not occurred (A' has occured), then 1-X=1 and 1-X=0 otherwise.

Similarly, 1-Y is an indicator function of B'

max(X,Y) is an indicator function of AUB (union of the two events). If either A or B or both has occurred (AUB), then max(X,Y) = 1 and if both A and B has not occurred, max(X,Y) =0

XY is an indicator function of A∩B (intersection of the two events). If both A and B has occurred (A∩B), then XY = 1 and if either A or B or both has not occurred, XY =0

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