Probability (1) introduction

# Probability (1) introduction - Probability Originate from...

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Probability • Originate from the study of games of chance and gambling during the 16th century. God of gamblers Rank of Poker Hands

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Probability • Originate from the study of games of chance and gambling during the 16th century. Although we cannot exactly predict what we get in any random phenomena, say heads or tails when flip a coin, through the notion of probability, we can find the regularity of these random phenomena , say if we keep flipping a coin many many times, then the ratio of the number of heads occurs to the total number of flipping will go to ½. The theory of probability plays an important role of the study of random phenomenon, and also provides a theoretical framework of statistical research. • Be a measure of the possibility that a random phenomenon occurs, e.g. the tossing of a dice.
Random phenomenon and random experiment Under some certain conditions, if the phenomenon may occur or may not occur , then it is called a random phenomenon . For example, if we flip a fair coin, head may be observed or may not be observed. Under the same conditions, if the experiment (i.e. a process that generates a set of data) can be repeated , and all possible outcomes in the experiment are KNOWN but each outcome cannot be determined with certainty at each time before the experiments are performed , then we call the experiment a random experiment . Say, the tossing of a coin.

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Basics of probability theory The set/collection of ALL possible outcomes of a random experiment is called the sample space , usually denoted by the symbol S or Ω. Each outcome of the sample space is called a sample point or an element .
Sample Space Sample spaces can be classified according to the number of sample points they contain. If the sample space has a finite number of elements, then we may list all the elements separated by commas and enclosed in braces. For instance, if we toss a fair coin, then the sample space S = { H, T } where H and T represent head or tail, respectively

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Sample Space Sample spaces can be classified according to the number of sample points they contain.
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