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# 数学代写|概率论代考Probability Theory代写|STAT7614 THE GENERAL CONSTRUCTION OF THE PROBABILITY SPACE

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## 数学代写|概率论代考Probability Theory代写|THE GENERAL CONSTRUCTION OF THE PROBABILITY SPACE

We have considered the variants of probabilistic spaces in situations where the number of outcomes of some experiment is finite or even countable. It should be noted that such schemes are very popular. Elementary events in such situations may be, for example, the following:
“the appearance of the six when throwing a die,”
“getting a ticket with the number 7 during a random selection of 24 examination tickets,”
“three defeats of a football team before its first victory in the championship,”
“the five-time appearance of the letter ” $s$ ” on the first page of a readable newspaper,”
“the winning combination of numbers $(2,8,11,22,27,31)$ falls out in the draw of a lotttery.”
However, many experiments do not fit into these discrete schemes. For example, the result of some experiment may be the coordinate of a randomly thrown point on a real line or the coordinates of a randomly thrown point on a unit square. Therefore, a further generalization of our construction of probability spaces must be useful.

## 数学代写|概率论代考Probability Theory代写|RANDOM VARIABLES AND DISTRIBUTION FUNCTIONS

Any probabilistic space constructed is inherently a card file in which a certain set of events and a set of probabilities corresponding to them are located, which determine the degrees of opportunities for the appearance of these events. In many cases, these probabilities could be found without building such heavy construction, which is a probabilistic space, but it turns out that this construction is necessary for defining and working with such important probabilistic object, which is a random variable.

The fact is that very often random outcomes of some experiment completely unrelated to any numbers or numbering can determine certain numerical characteristics depending on these outcomes.

Let’s give the simplest example. The International Football Federation (FIFA) is going to use a lot to determine where the qualifying match of the world championship between the teams of Russia and Finland will take place. The drum contains three cards with the names of the stadiums in St. Petersburg, Helsinki and the neutral field in Berlin. A randomly selected card must determine the city in which this match will take place. A fan from St. Petersburg who is going to visit this game without fail assesses his future expenses (depending on the choice of one of these three stadiums), respectively, as 3,000, 10,000 and 20,000 rubles. For him, before the draw, the future cost is a random variable, taking one of these three values with equal probabilities $1 / 3$.

# 概率论代写

## 数学代写|概率论代考Probability Theory代写|THE GENERAL CONSTRUCTION OF THE PROBABILITY SPACE

“掷骰子时出现 6″、
“在随机抽取 24 张考试票时得到一张数字为 7 的票”、
“足球输了 3 次”首胜前的球队”、
“五次出场的信” $s$ ” 在可读报纸的第一页上，”

## 数学代写|概率论代考Probability Theory代写|RANDOMVARIABLES AND DISTRIBUTION FUNCTIONS

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