Statistics Assignment Help>>离散且连续的概率分布

Probability

The word probability is derived from the Latin word probabilitias which means probity. It is used for describing an attitude of mind for some proposition of whose truth or result we are not certain about. Higher probability for any event means there is more certainty to the occurring of event. Hence, the use of probability in applied sense is meant to measure the likeliness of the occurring of an event.

概率理论是涉及随机现象的数学分支。概率理论集中在随机变量，随机事件和过程上。概率理论在人类活动中至关重要，该活动涉及较大数据集的定量分析。物理学是对原子量表发生的物理现象的概率性质的研究，并通过量子力学描述。

Probability of an event- an event is termed as a given set of outcomes for which the probability is assigned. Since the sample space is finite, any subset in the sample space can be said to be an event. For example, in an assembly of 52 playing cards in a deck having no jokers, the sample space is a 52-element set and if we draw a single card from the deck then withdrawing of each card is a possible outcome. But the event is a subset of the sample space and may include a singleton set or elementary event, an empty set, a possible event and even the sample space.

有条件的概率- It is the probability of any event in a particular set of given circumstances. In more formal terms, a conditional probability can be termed as the occurring of event A when the sample space is limited to the event B. The conditional probability is denoted by P (A/B) and is read as ‘the probability of A, given b’.

Discrete and continuous probability distributions-概率质量，概率分布或概率密度是一个函数，它通过采取和假设值来描述任何随机变量的概率。在离散概率分布中，此随机变量是离散变量。例如，翻转硬币两次给出四个可能的结果，即HH，HT，TH和TT（头部和尾部的h）。如果随机变量x表示导致实验的头部数，则可以仅以0、1或2的值为单位，因此是离散的随机变量。在连续概率分布中，随机变量是连续变量。该连续变量与离散变量不同，因为连续变量可能假定任何特定值为零的概率。因此，连续概率分布不能以表格形式表示，而是通过使用方程式或公式来描述。

历史of probability theory

The roots of the mathematical theory of probability can be found in the attempts made for analyzing the game of chance by the mathematician Gerolamo Cardano in the early sixteenth century. The contribution of Pierre de Fermat and Blasé Pascal in the problem of points had some important repercussions on the theory of probability. A full book on the subject was published by Christian Huygens in the year 1657. In the beginning, probability theory included only the discrete events but the analytical considerations led to the incorporation of the continuous variables in the probability theory. The modern probability theory has its foundation laid by Andrei Nikolayevich Kolmogorov, who presented his axiom system of probability in the year 1933 by combining the notion of sample space (given by Richard von Mises) and the measure theory. Later Bruno de Fineti combined the finite additivity in place of the countable additivity with the theory, and gave another alternative to the probability theory.

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