DISJOINT OR MUTUALLY EXCLUSIVE EVENTS

Two events are independent if the occurrence of one event gives no information about the occurrence of the other event. The two events, A and B, are independent if the probability that they both occur is equal to the product of the probabilities of the two individual events: P(A, B) = P(A)P(B). Two events are disjoint or mutually exclusive if the occurrence of one is incompatible with the occurrence of the other, i. e., if they cannot both happen at once (if they have no outcome in common). Equivalently, two events are disjoint if their intersection is the empty set.

B11 EXPECTATION

The expected value of a random variable is the long-term average of its values. For a discrete random variable (one that has a countable number of possible values), the expected value is the weighted average of its possible values, and the weight assigned to each possible value is the chance/probability that the random variable takes that value. The mathematical expectation E(x) = ^”= 1 x, P(x = x,) and E(x) = J1 xp(x)dx with P as the probability distribution of variables x and p the PDF of variable x. It is a weighted mean and the weights are individual probabilities. The expected value of the sum of two variable is the sum of their expected values E(X + Y) = E(X) + E( Y), similarly E(a x X) = a x E(X).