问一道题：NO.PZ2020011303000049

NO.PZ2020011303000049问题如下 investment hprobabilities of 0.1, 0.3, 0.2, 0.3, an0.1 of giving one-yereturns equto 30%, 20%,10%, 0%, an-10%.Suppose ththere are two investments with the same probability stribution of returns above. Whis the totmeanstanrviation of returns if the correlation between them is 0.2? The totmereturn is 10%. The expectesquarereturn is 0.024 so ththe stanrviation of the return is 0.024−0.12=0.014=0.118\sqrt{0.024-0.1^2}=\sqrt{0.014}=0.1180.024−0.12​=0.014​=0.118 or 11.8% stanrviation of returns is 0.52×0.1182+0.52×0.1182+2×0.5×0.5×0.118×0.118×0.2=0.0914\sqrt{0.5^2\times0.118^2+0.5^2\times0.118^2+2\times0.5\times0.5\times0.118\times0.118\times0.2}=0.09140.52×0.1182+0.52×0.1182+2×0.5×0.5×0.118×0.118×0.2​=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？expectesquareeturn=0.1*(30%)^2+0.3*(20%)^2+0.2*(10%)^2+0.3*(0%)^2+0.1*(-10%)^2=0.024stanrviation ofreturn=(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% 还是不懂tot10咋求出来的 还有那个0.5和0.118怎么得的

NO.PZ2020011303000049 为什么总的variance不是2*（1+correlation coefficient）*单个的variance？

数学太差，这个expectesquarereturn is 0.024是怎么来的？ 这个求标准差的公式 \sqrt{0.024-0.1^2}=\sqrt{0.014}=0.118也不明白。