**Linearity of Expected Value:** Suppose and are random variables and and are scalars. The following relationships hold:

**Variance:**

Suppose for are independent identically distributed (iid) random variables. Then for and

**Example:**

is the stock price of AAPL at market close. is the sum of closing AAPL stock prices for 5 days. Then

.

Contrast this with the variance of . In other words, is a random variable that takes a value of 5 times the price of AAPL at the close of any given day. Then

The distinction between and is subtle but very important.

**Variance of a Sample Mean:**

In situations where the sample mean is a random variable over iid observations (i.e. the average price of AAPL over 5 days), the following formula applies: