随机变量及分布函数，一起学习随机变量的分布函数

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在实际中，对于一些随机变量，我们会考虑误差落在某个区间内的概率，下面引入随机变量的分布函数的概念。

In practice, for some random variables, we will consider the probability that the error falls within an interval, and we introduce the concept of the distribution function of the random variables below.

因此,若已知X的分布函数，我们就知道X落在任一区间上的概率， 从这个意义上说,分布函数完整地描述了随机变量的统计规律性.

分布函数是一个普通的函数，正是通过它，我们将能用数学分析的方法来研 究随机变量.

分布函数F（X）具有以下的基本性质：

Therefore, if the distribution function of X is known, we know the probability of X falling on any interval, and in this sense, the distribution function completely describes the statistical regularity of the random variables.

The distribution function is an ordinary function, and it is through it that we will be able to study random variables by mathematical analysis.

The distribution function F (X) has the following basic properties:

上面两个式子，我们只从几何上加以说明.在将区间端点x沿数轴无限向左移动(即x→ -∞)，则“随机点X落在点x左边”这一事件趋于不可能事件， 而其概率趋于0，即有F(-∞)=0;又若将点x无限右移(即→∞),则“随机点X落在点x左边”这一事件趋于必然事件，从而其概率趋于1,即有F(oo)=1.

3°F(x 0)=F(x),即F(x)是右连续的。

The above two formulas, which we illustrate only geometrically. Moving the interval end point x infinitely left along the number axis (i. e., x-), the event "the random point X falls to the left of the point x" tends to be the impossible event, The probability goes to 0, namely F (-) =0; if the point x is infinitely right the event "random point X falls to the left of point x" tends to an inevitable event, so its probability tends to 1, that is, F (oo) =1.

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参考资料：《概率论与数理统计 》

翻译：金山词霸

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