小女不才，是微观经济学的初学者，目前遇到一道题，希望大家帮忙解决一下，好人一生平安，谢谢大家。最好希望能有解释或者过程
Firm A sells lemonade and firm B sells hot chocolate. If you invest $100 f firm A, in one year you will get back $(30 +
T ) where T is the average temperature (Fahrenheit) during the summer. If you invest $100 in firm B, in one year you
will get back $(150-T ), where T is the average temperature during the summer. The expected value of T is 70 and the
standard deviation of T is 10. If you invest $50 in firm A and $50 in firm B, what is the standard deviation of your
return on your investment?
A. 10
B. 5
C. 0
D. 20
E. None of the above.
total return: 0.5(30+T)+0.5(150-T)=90
so the standard deviation of your return on your investment is 0.
if the investment change,the result is different.
80美元投资柠檬，20美元投资巧克力
total return:0.8（30+T)+0.2(150-T)=0.6T+54
总投资回报的标准差是0.6*10=6
如果投资柠檬所占比例为x(0<x<1)
总回报：x(30+T)+(1-X)(150-T)=2xT-T-120x+150
D(2xT-T-120x+150)=(2x-1)^2D(T)
故其标准差为20x-10的绝对值
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