<meta http-equiv="refresh" content="1; url=/nojavascript/"> Sums and Differences of Independent Random Variables ( Study Aids ) | Probability | CK-12 Foundation

# Sums and Differences of Independent Random Variables

%
Best Score
Practice Sums and Differences of Independent Random Variables...
Best Score
%
Transforming Random Variables
0  0  0

When you add or subtract a constant from the outcomes of a random variable, the mean will increase or decrease by that amount, and the standard deviation will stay the same.

Example:  This distribution is called X.

$\mu_X &=3 \\\sigma_X &=1$

If we add 2 to the distribution, it becomes X + 2.  Now the distribution has a mean of 5, but the standard deviation is still 1:

$\mu_{X+2} &=5 \\\sigma_{X+2} &=1$

When you multiply or divide the outcomes of a random variable by a constant, the mean and the standard deviation will also be multiplied or divided by that constant.

Example: This distribution is called $Y$.
$\mu_Y=3$
$\sigma_Y=1$

Let’s see what happens if we multiply each outcome by 3, and find $\mu_{3Y}$ and $\sigma_{3Y}$ :

$\mu_{3Y} = 3 \times 3=9$

$\sigma_{3Y}=1 \times 3=3$