SkipperLin · 2020年02月10日
问题如下：
If X1 and X2 both have univariate normal distributions, is the joint distribution of X1 and X2 a bivariate normal?
选项：
解释：
Not necessarily.
It is possible that the joint is not a bivariate normal if the dependence structure between X1 and X2 is different from what is possible with a normal. The distribution that generated the data points plotted below has normal marginals, but this pattern of dependence is not possible in a normal that always appear elliptical.
可以解释一下答案么
pzqa27 · 2024年09月02日
嗨，从没放弃的小努力你好：
在这两个变量各自服从正态分布的情况下，它们的联合分布不一定是正态分布，主要原因是这两个变量之间的相关性或依赖性。
这意味着无论是 X 还是 Y，它们的边缘分布都是钟形对称的，具有固定的均值和方差。
如果 X 和 Y 都服从正态分布，但它们之间的关系是非线性的，那么联合分布可能不再是正态分布。例如：
此时，联合分布不再是标准的二维正态分布，而会呈现非对称或其他复杂形状。
----------------------------------------------就算太阳没有迎着我们而来，我们正在朝着它而去，加油！
NO.PZ2020010304000008问题如下 If X1 anX2 both have univariate normstributions, is the joint stribution of X1 anX2 a bivariate normal?Not necessarily. It is possible ththe joint is not a bivariate normif the pennstructure between X1 anX2 is fferent from whis possible with a normal. The stribution thgeneratethe ta points plottebelow hnormmarginals, but this pattern of pennis not possible in a normthalways appeelliptical.“两个变量各自服从正态分布，这两个变量的联合分布不一定服从正态分布，得有前提条件就是它们是互相独立的或者相关性为0（事实上相关性为0就可以了，互相独立的条件更强）。”老师好，这里的“事实上相关性为0就可以了”是指p，也就是无线性关系就行？
NO.PZ2020010304000008 问题如下 If X1 anX2 both have univariate normstributions, is the joint stribution of X1 anX2 a bivariate normal? Not necessarily. It is possible ththe joint is not a bivariate normif the pennstructure between X1 anX2 is fferent from whis possible with a normal. The stribution thgeneratethe ta points plottebelow hnormmarginals, but this pattern of pennis not possible in a normthalways appeelliptical. 这道题是什么意思？考点是什么？
NO.PZ2020010304000008 问题如下 If X1 anX2 both have univariate normstributions, is the joint stribution of X1 anX2 a bivariate normal? Not necessarily. It is possible ththe joint is not a bivariate normif the pennstructure between X1 anX2 is fferent from whis possible with a normal. The stribution thgeneratethe ta points plottebelow hnormmarginals, but this pattern of pennis not possible in a normthalways appeelliptical.
翻一下答案
