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Essay On Statistical Regularity

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Introduction to Probability

Randomness and statistical regularity
There are many instances in nature for which we cannot predict the possible event that may happen. We can say in these cases that the occurrence of the event is random. However for whatever reason that the event cannot be predicted we can make a definite average pattern of results can be seen in these situations leading to random occurrences when the situation that led to the event is repeated a number of times.
The simplest example for this would be if a coin is flipped many times, for roughly half of the flips it shall turn up heads. Probability measures the likelihood of an event occurring.

Statistical regularity is the tendency of repeated experiments for the pattern
…show more content…
An experiment can be considered random when there is little precision in which we can determine the possible outcomes of the experiment. The frequency of an outcome occurring can be determined by the fraction: f_N (A)= (N(A))/N
Where A is one of the possible outcomes of the experiment, N is the integer number of times we repeat the experiment and N(A) is the number of times that outcome A occurs. If there is a certainty that the relative frequency will go to a limit as N increases then we can say that the outcome A has a definite probability of occurring.

The Axioms of Probability
The sample space is a mathematical collection of all possible experimental outcomes.
An object in a sample space is called a sample point. Each sample point, therefore, corresponds to a possible outcome of an experiment. An event is a set of sample points. Event A is the set of all sample points such that certain conditions on the sample points are satisfied. Therefore, an event is a subset of the sample space.

A probability measure is an assignment of real numbers to the events defined on the collection of all possible experimental outcomes.
The probability of an event A occurring is denoted by

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