std的结果

问题如下：

How are the mean, standard deviation, and variance of Y related to these values of X when Y = a + bX?

选项：

解释：

E[Y] = E[a + bX] = E[a] + E[bX]Expectation of sum is the sum of expectations

= a + bE[X] Expectation of a constant is constant.

The variance of Y is $V[a + bX] = V[bX] = b^2V[X]$ because the variance of a constant is 0 and the variance of bX is $b^2$ times the variance of X.

The standard deviation of Y is simply the square root of the variance given above, $\sqrt{b^2V[X]} = |b|\sqrt{V[X]}$.