In the case of continuous variables, each (possible) event has a non-zero probability of occurring, but it is so small that only the probability distribution makes it possible to measure it. In the case of discrete variables, each event has a non-zero probability as long as it is possible. In this case, we will match the event "there are 10 people queuing" with the number 10, or "the temperature is 59.8☏" with the real number 59.8. While this is perfectly arbitrary in the case of a coin, it may be more natural if one counts the number of people in a queue at the post office, or if one measures the air temperature. For example, we can match the tossing of a coin with 0 if the coin lands on head, and 1 if the coin lands on tail. Nevertheless, it is so complex that it is preferable to estimate that each face has a certain probability of being the result of the throw and that the occurrence of an event is random.Ī random variable is also a function that maps an event to a real number. When you roll a dice, a perfect knowledge of the starting movement allows you to know when, where, and in what position the dice would stop. Randomness is a representation of ignorance or imperfect knowledge. Many probability distributions have been developed to describe particular situations where randomness occurs. A common example when learning to calculate the probability is calculating the chances of winning a game, which often corresponds to the proportion of winning outcomes over the total number of outcomes. It allows us to relate events (for example, the occurrence of a 2 when throwing a dice), to the probability of a said event occurring. A probability distribution is a special type of function, that is named a measure in mathematics.
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