We are ready to now formally give a name to the theoretical measure of expectation for outcomes from an experiment. Taking our cue from our examples, let’s make our definition agree with the following relative frequency properties:
Relative frequency cannot be negative, since cardinality cannot be negative
Relative frequencies for complementary events should sum to one and for disjoint events these relative frequencies should simply accumulate.
Relative frequencies for collections of disjoint outcomes should equal the sum of the individual relative frequencies