<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
Dismiss
Skip Navigation
Our Terms of Use (click here to view) and Privacy Policy (click here to view) have changed. By continuing to use this site, you are agreeing to our new Terms of Use and Privacy Policy.

Sums and Differences of Independent Random Variables

Horizontal and vertical translations of the histogram

Atoms Practice
Estimated10 minsto complete
%
Progress
Practice Sums and Differences of Independent Random Variables
Practice
Progress
Estimated10 minsto complete
%
Practice Now
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*} 

My Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes
Please to create your own Highlights / notes
Show More

Image Attributions

Explore More

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