Variance怎么求的 谢谢

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 $2X_1+2X_2+0.5X_3+0.5X_4$

解释：

The expectation is

E[2X1+2X2+0.5X3+0.5X4]

=2u+2u+0.5u+0.5u

=5u=5.

The variance is

Var[2X1+2X2+0.5X3+0.5X4]

=4Var[X1]+4Var[X2]+0.25Var[X3]+0.25Var[X4]

=2+2+0.5+0.5

=5