还是不太懂total mean value 10是咋来的

问题如下：

An investment has probabilities of 0.1, 0.3, 0.2, 0.3, and 0.1 of giving one-year returns equal to 30%, 20%,10%, 0%, and -10%.

Suppose that there are two investments with the same probability distribution of returns as above. What is the total mean and standard deviation of returns if the correlation between them is 0.2?

解释：

The total mean return is 10%.

The expected squared return is 0.024 so that the standard deviation of the return is $\sqrt{0.024-0.1^2}=\sqrt{0.014}=0.118$ or 11.8%

standard deviation of returns is $\sqrt{0.5^2\times0.118^2+0.5^2\times0.118^2+2\times0.5\times0.5\times0.118\times0.118\times0.2}=0.0914$ or 9.14%

有一个投资产品获得30%回报率的可能性是0.1，20%回报率的可能性是0.3，10%回报率的可能性是0.2，0%回报率的可能性是0.3，-10%回报率的可能性是0.1。

假设有两个投资具有与上述相同的收益概率分布。 如果它们之间的相关性为 0.2，则回报的总均值和标准差是多少？

expected squared return=0.1*(30%)^2+0.3*(20%)^2+0.2*(10%)^2+0.3*(0%)^2+0.1*(-10%)^2=0.024

standard deviation of return=(0.5^2×0.118^2+0.5^2×0.118^2+2×0.5×0.5×0.118×0.118×0.2)^0.5=0.0914 or 9.14%