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Mutually Exclusive Events
Two or more events which cannot happen at the same point of time are called as mutually exclusive events.
If two or more events cover the entire sample space i.e. if two or more events cover all possible outcomes of an experiment, then such events are called as exhaustive events.
If probability of an happening of an event is 1, the event is a certain event.
If probability of an happening of an event is o, the event is an impossible event.
Complement of an event.
Complement of an event means that event does not happen. i.e. if event A is getting 1 in a throw of dice then A complement is not getting 1 in a throw of dice. Complement of event A is denoted by (Ac ,A | or ) And P(Ac) = 1 — P(A).
Expectation, Expected Value.
For discrete distribution expected value is weighted means of all outcomes where weights are probability of the outcome.
For continuous distribution expected value the mean value.
If X and Y are two random variables, the expected value of their sum is the sum of their expected values (E(X+Y) = E(X) + E(Y)), and the expected value of a constant a times a random variable X is the constant times the expected value of X (E(aÃ—X ) = aÃ— E(X)).