累计概率密度还是不太会看可以帮忙再具体解释下吗？

NO.PZ2023091601000013

问题如下：

The following graphs show the cumulative distribution function (CDF) of four different random variables. The dotted vertical line indicates the mean of the distribution. Assuming each random variable can only be values between -10 and 10, which distribution has the highest variance?

选项：

解释：

Variance is a measure of the mean deviation. In the above four graphs, it can be seen that D has the highest proportion of the distribution that deviates from the mean, and it also has a relatively higher density in both tails. Hence, D has the highest variance.

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李坏_品职助教 · 2025年02月20日

嗨，爱思考的PZer你好：

图的纵轴不太清晰，纵坐标写的是CDF，cumulative distribution function，也就是累计概率密度。

随着横坐标X的值越来越大，4个图片里面的CDF都是变大的，但是D选项在横轴左侧的CDF最高（说明X的极小值在D选项里概率很大），而且D选项右侧一直到很大的X依然有较高的曲线斜率（说明X极大时，CDF依然在快速增加，X的极大值在D选项里概率也很大）。这说明无论是极小还是极大的X值，在D选项的概率都很高。

而ABC选项，左侧（X很小时）的CDF较低，右侧（X很大时）的CDF变动的斜率也在下降，所以都不如D的方差大。题目最后问which distribution has the highest variance? D选项有最大的方差，选D。

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2024-04-11 19:16 2 · 回答

累计概率密度还是不太会看 可以帮忙再具体解释下吗？

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累计概率密度还是不太会看可以帮忙再具体解释下吗？