No.PZ2020010303000008 (问答题)
来源: 原版书
How are the mean and variance of a mixture of normal random variables related to the mean and variance of the components of the mixture?
解析
The mean is the weighted average of the means of the components. The variance is more complicated. The second non-central moment, E[X^2] of the mixture is the weighted average of the second non-central moments of the components. The variance is then E[X^2] - E[X]^2
, which depends the first and second moments of the mixture.
normal random的话不是mean=0么？那么weighted average of means不是应该也是0？
var也不是很明白，不是应该是之前学到的和协方差相关的一个公式么？
