离散型随机变量分布函数性质证明

f(x)=p{x<=x}，p{x<=x}=limp{x<=x+delta
x}(当delta
x右趋于零)，
从而f(x)可表为自身的于点x处的右侧极限，f(x)右连续
离散型随机变量的累积分布函数图像呈阶梯状
所以f(x)在非间断点处处连续，在间断点(基本空间中的事件点对应随机变量取值)处仅左连续
这里f(x)即是分布列（对应连续型随机变量的密度函数），基本空间（必然事件）对应一离散点列（离散随机变量所有可取的值），所以f(1-0)不存在
因为是右连续，所以x取不到5，相应的f(x)也累积不到x=5这一点的概率密度，所以是1/10+3/10

It is depends on how you define your cumulative distribution function (cdf)...
In some textbook, they define the cdf as:
F(x)=P(X<x), then this function should be left continuous
In some other books, you may see the def of cdf is:
F(x)=P(X<or=x), then the function should be right continuous
This problem is not just for discrete random variables, but this difference in definition has a larger influence to discrete r.v., because for discrete r.v., the probability is not zero for a single point, i.e. P(X=x) is not 0, while it is 0 for continuous r.v.