Statistical Probability (or a posteriori probability)

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Statistical Probability (or a posteriori probability) 2018-03-26T11:30:55+00:00

If the probability of an event can be determined only after the actual happening of the event, it is called Statistical probability. If an event occurs m times out of n, its relative frequency is m/n. In the limiting case, when n becomes sufficiently large it corresponds to a number which is called the probability of that event.

In symbol, P(A) = Limit (m/n) n → ∞

The above definition of probability involves a concept which has a long term consequence. This approach was initiated by the mathematician Von Mises . If a coin is tossed 10 times we may get 6 heads and 4 tails or 4 heads and 6 tails or any other result. In these cases the probability of getting a head is not 0.5 as we consider in Mathematical probability. However, if the experiment is carried out a large number of times we should expect approximately equal number of heads and tails and we can see that the probability of getting head approaches 0.5. The Statistical probability calculated by conducting an actual experiment is also called a posteriori probability or empirical probability.

 

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