<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />

# Sums and Differences of Independent Random Variables

## Horizontal and vertical translations of the histogram

Estimated10 minsto complete
%
Progress
Practice Sums and Differences of Independent Random Variables

MEMORY METER
This indicates how strong in your memory this concept is
Progress
Estimated10 minsto complete
%
Transforming Random Variables

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.

\begin{align*}\mu_X &=3 \\ \sigma_X &=1\end{align*}

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:

\begin{align*}\mu_{X+2} &=5 \\ \sigma_{X+2} &=1\end{align*}

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 \begin{align*}Y\end{align*}.
\begin{align*}\mu_Y=3\end{align*}
\begin{align*}\sigma_Y=1\end{align*}

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

\begin{align*}\mu_{3Y} = 3 \times 3=9\end{align*}

\begin{align*}\sigma_{3Y}=1 \times 3=3\end{align*}

### Explore More

Sign in to explore more, including practice questions and solutions for Sums and Differences of Independent Random Variables.