论文标题
关于平均移动高斯分布的有条件期望
On the Conditional Expectation of Mean Shifted Gaussian Distributions
论文作者
论文摘要
在本文中，我们考虑了单变量高斯分布的特性，即有条件期望转移（或质心变化）。具体来说，我们比较了两个高斯分布，其中它们仅在手段上有所不同。同等地，我们可以将这种情况视为分布之一向右移动。这两个分布的条件是在相同的事件下，在相同的事件中，实现属于正确的间隔或左间隔。我们表明，如果高斯分布向右移动，而条件事件则保持不变，则有条件的期望会同时转移到右侧。
In this paper, we consider a property of univariate Gaussian distributions namely conditional expectation shift (or centroid shift). Specifically, we compare two Gaussian distributions in which they differ only in their means. Equivalently, we can view this situation as one of the distribution is shifted to the right. These two distributions are conditioned on the same event in which the realizations fall in the right interval or left interval. We show that if a Gaussian distribution is shifted to the right while the conditioning event remains the same then the conditional expectation is shifted to the right concurrently.
