NO.PZ2020010304000033
问题如下：
Suppose four independent random variables X1, X2, X3, and X4 all have mean u = 1 and variances of 0.5, 0.5, 2, and 2, respectively.
Compute the expectation and variance of
解释：
The expectation is computed
E[0.4X1+0.4X2+0.1X3+0.1X4]
=0.4EX1+0.4EX2+0.1EX3+0.1EX4
=0.4u+0.4u+0.1u+0.1u
=u=1
This estimator is unbiased.
The variance of the sum is the sum of the variances because the random variables are independent.
Var[0.4X1+0.4X2+0.1X3+0.1X4]
=0.16Var[X1]+0.16Var[X2]+0.01Var[X3]+0.01Var[X4]
=0.16*0.5+0.16*0.5+0.01*2+0.01*2
=0.2
为什么不平方x1的variance0.5，而是平方前面的加权平均数0.4呢？是因为variance是随机变量吗，他才是那个加权平均数？
