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比如世界 · 2020年03月20日

问一道题:NO.PZ2020011303000130

问题如下:

X and Y are variables that have uniform distributions between 0 and 1 (a uniform distribution is a distribution where all values in a certain range are equally likely). A Gaussian copula model is used to define a correlation between them. The correlation parameter is 0.25. How would you determine the probability that both are less than 0.5?

选项:

解释:

In the Gaussian copula model, the 0.5 values for X is transformed to the zero value of a standard normal distribution. The same is true for Y. The required probability is the probability that the first variable is less than zero, and the second variable is less than zero in a bivariate normal probability distribution where the coefficient of correlation is 0.25 (it can be shown that this is about 0.29).

老师您好,这道题题目和答案的意思不是很明白,题目告诉了相关系数,要求的是概率吗?答案解析的是啥?谢谢

1 个答案

小刘_品职助教 · 2020年03月21日

同学你好,这道题超纲了,大概了解就行。

主要要理解Gaussian copula model的过程,因为原来的X和Y是满足均匀分布的,通过Gaussian copula的过程,把他转化为两个正态分布,答案中以0.5为例,原来均匀分布中X=0.5,经过copula这个过程中转化为0。之后的话通过二维正态分布将X和Y之间的相关关系求出是0.25。

如果是相关系数为0的话就比较好求,X和Y同时小于0.5的概率就是0.25,现在有相关关系的计算过程比较复杂,可以不用关注了。

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