(a) If and are independent, then by observing that .

(b)
In contrast to the expectation,
the variance is *not* a linear operator.
For two random variables and , we have

However, if and are independent, by observing that in (), we have

In general, when we have a sequence of independent random variables , the property () is extended to

**Variance and covariance under linear transformation.**
Let and be scalars (that is, real-valued constants),
and let be a random variable.
Then the variance of is given by

Generated by MATH GO: 2005-09-15