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Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.Two events are independent, statistically independent, or stochastically independent [1] if, informally speaking, the occurrence of one does not affect the probability of occurrence of the other or, equivalently, does not affect the odds.
In logic, two propositions and are mutually exclusive if it is not logically possible for them to be true at the same time; that is, () is a tautology. To say that more than two propositions are mutually exclusive, depending on the context, means either 1. "() () is a tautology" (it is not logically possible for more than one proposition to be true) or 2. "() is a tautology" (it is not ...
If either event A or event B can occur but never both simultaneously, then they are called mutually exclusive events. If two events are mutually exclusive, then the probability of both occurring is denoted as () and = = If two events are mutually exclusive, then the probability of either occurring is denoted as () and = = + () = + = + ()
The mutually exclusive event {5} has a probability of 1/6, and the event {1,2,3,4,5,6} has a probability of 1, that is, absolute certainty. When doing calculations using the outcomes of an experiment, it is necessary that all those elementary events have a number assigned to them. This is done using a random variable.
A random experiment that has exactly two (mutually exclusive) possible outcomes is known as a Bernoulli trial. [ 2 ] When an experiment is conducted, one (and only one) outcome results— although this outcome may be included in any number of events , all of which would be said to have occurred on that trial.
Independent: Each outcome of the die roll will not affect the next one, which means the 10 variables are independent from each other. Identically distributed : Regardless of whether the die is fair or weighted, each roll will have the same probability of seeing each result as every other roll.
In probability theory, an outcome is a possible result of an experiment or trial. [1] Each possible outcome of a particular experiment is unique, and different outcomes are mutually exclusive (only one outcome will occur on each trial of the experiment). All of the possible outcomes of an experiment form the elements of a sample space. [2]
This can be represented mathematically as follows: If a random experiment can result in N mutually exclusive and equally likely outcomes and if N A of these outcomes result in the occurrence of the event A, the probability of A is defined by =. There are two clear limitations to the classical definition. [18]