请教关于u的问题

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 $0.4X_1+0.4X_2+0.1X_3+0.1X_4$

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