Combining random variables worksheet

Means add and subtract just as the variables do. For independent variables the variances always add, even for a difference, so the standard deviation is the square root of the sum of squares.

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Sigma Prep · sigmaprep.io/worksheets Name Combining Random Variables Date Period Answer each question. $X$ has mean 20 and standard deviation 8. Find the mean and standard deviation of $W = 3 X + 30$ . $X$ has mean 34 and standard deviation 3; $Y$ has mean 8 and standard deviation 4, and they are independent. Find the mean and standard deviation of $X + Y$ . $X$ has mean 24 and standard deviation 2; $Y$ has mean 13 and standard deviation 3, and they are independent. Find the mean and standard deviation of $X - Y$ , the standard deviation to the nearest hundredth. $X$ has mean 15 and standard deviation 9. Find the mean and standard deviation of $W = - 5 X + 30$ . $X$ has mean 17 and standard deviation 2; $Y$ has mean 19 and standard deviation 3, and they are independent. Find the mean and standard deviation of $X + Y$ , the standard deviation to the nearest hundredth. $X$ has mean 23 and standard deviation 3; $Y$ has mean 7 and standard deviation 4, and they are independent. Find the mean and standard deviation of $X - Y$ . $X$ has mean 56 and standard deviation 11. Find the mean and standard deviation of $W = 2 X - 18$ . $X$ has mean 14 and standard deviation 6. Find the mean and standard deviation of $W = - 3 X - 4$ . $X$ has mean 37 and standard deviation 8; $Y$ has mean 8 and standard deviation 15, and they are independent. Find the mean and standard deviation of $X - Y$ . $X$ has mean 40 and standard deviation 4; $Y$ has mean 31 and standard deviation 7, and they are independent. Find the mean and standard deviation of $X - Y$ , the standard deviation to the nearest hundredth. $X$ has mean 23 and standard deviation 10. Find the mean and standard deviation of $W = 5 X + 23$ . $X$ has mean 53 and standard deviation 3; $Y$ has mean 13 and standard deviation 4, and they are independent. Find the mean and standard deviation of $X + Y$ . $X$ has mean 52 and standard deviation 7. Find the mean and standard deviation of $W = - 2 X - 17$ . $X$ has mean 18 and standard deviation 2; $Y$ has mean 13 and standard deviation 3, and they are independent. Find the mean and standard deviation of $X + Y$ , the standard deviation to the nearest hundredth. $X$ has mean 50 and standard deviation 5. Find the mean and standard deviation of $W = 5 X - 12$ . $X$ has mean 5 and standard deviation 8. Find the mean and standard deviation of $W = - 5 X + 30$ . $X$ has mean 14 and standard deviation 3. Find the mean and standard deviation of $W = - 3 X + 14$ . $X$ has mean 41 and standard deviation 7. Find the mean and standard deviation of $W = - 2 X - 1$ . $X$ has mean 27 and standard deviation 6. Find the mean and standard deviation of $W = 2 X + 26$ . $X$ has mean 47 and standard deviation 4; $Y$ has mean 18 and standard deviation 7, and they are independent. Find the mean and standard deviation of $X + Y$ , the standard deviation to the nearest hundredth. Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Combining Random Variables

Date Period

Answer each question.

$X$ has mean 20 and standard deviation 8. Find the mean and standard deviation of $W = 3 X + 30$ .
$X$ has mean 34 and standard deviation 3; $Y$ has mean 8 and standard deviation 4, and they are independent. Find the mean and standard deviation of $X + Y$ .
$X$ has mean 24 and standard deviation 2; $Y$ has mean 13 and standard deviation 3, and they are independent. Find the mean and standard deviation of $X - Y$ , the standard deviation to the nearest hundredth.
$X$ has mean 15 and standard deviation 9. Find the mean and standard deviation of $W = - 5 X + 30$ .
$X$ has mean 17 and standard deviation 2; $Y$ has mean 19 and standard deviation 3, and they are independent. Find the mean and standard deviation of $X + Y$ , the standard deviation to the nearest hundredth.
$X$ has mean 23 and standard deviation 3; $Y$ has mean 7 and standard deviation 4, and they are independent. Find the mean and standard deviation of $X - Y$ .
$X$ has mean 56 and standard deviation 11. Find the mean and standard deviation of $W = 2 X - 18$ .
$X$ has mean 14 and standard deviation 6. Find the mean and standard deviation of $W = - 3 X - 4$ .
$X$ has mean 37 and standard deviation 8; $Y$ has mean 8 and standard deviation 15, and they are independent. Find the mean and standard deviation of $X - Y$ .
$X$ has mean 40 and standard deviation 4; $Y$ has mean 31 and standard deviation 7, and they are independent. Find the mean and standard deviation of $X - Y$ , the standard deviation to the nearest hundredth.
$X$ has mean 23 and standard deviation 10. Find the mean and standard deviation of $W = 5 X + 23$ .
$X$ has mean 53 and standard deviation 3; $Y$ has mean 13 and standard deviation 4, and they are independent. Find the mean and standard deviation of $X + Y$ .
$X$ has mean 52 and standard deviation 7. Find the mean and standard deviation of $W = - 2 X - 17$ .
$X$ has mean 18 and standard deviation 2; $Y$ has mean 13 and standard deviation 3, and they are independent. Find the mean and standard deviation of $X + Y$ , the standard deviation to the nearest hundredth.
$X$ has mean 50 and standard deviation 5. Find the mean and standard deviation of $W = 5 X - 12$ .
$X$ has mean 5 and standard deviation 8. Find the mean and standard deviation of $W = - 5 X + 30$ .
$X$ has mean 14 and standard deviation 3. Find the mean and standard deviation of $W = - 3 X + 14$ .
$X$ has mean 41 and standard deviation 7. Find the mean and standard deviation of $W = - 2 X - 1$ .
$X$ has mean 27 and standard deviation 6. Find the mean and standard deviation of $W = 2 X + 26$ .
$X$ has mean 47 and standard deviation 4; $Y$ has mean 18 and standard deviation 7, and they are independent. Find the mean and standard deviation of $X + Y$ , the standard deviation to the nearest hundredth.



Sigma Prep · sigmaprep.io/worksheets Name Combining Random VariablesAnswer keyVersion 1 Date Period Answer each question. $X$ has mean 20 and standard deviation 8. Find the mean and standard deviation of $W = 3 X + 30$ .mean $90$ , SD $24$ $X$ has mean 34 and standard deviation 3; $Y$ has mean 8 and standard deviation 4, and they are independent. Find the mean and standard deviation of $X + Y$ .mean $42$ , SD $5$ $X$ has mean 24 and standard deviation 2; $Y$ has mean 13 and standard deviation 3, and they are independent. Find the mean and standard deviation of $X - Y$ , the standard deviation to the nearest hundredth.mean $11$ , SD $3.61$ $X$ has mean 15 and standard deviation 9. Find the mean and standard deviation of $W = - 5 X + 30$ .mean $- 45$ , SD $45$ $X$ has mean 17 and standard deviation 2; $Y$ has mean 19 and standard deviation 3, and they are independent. Find the mean and standard deviation of $X + Y$ , the standard deviation to the nearest hundredth.mean $36$ , SD $3.61$ $X$ has mean 23 and standard deviation 3; $Y$ has mean 7 and standard deviation 4, and they are independent. Find the mean and standard deviation of $X - Y$ .mean $16$ , SD $5$ $X$ has mean 56 and standard deviation 11. Find the mean and standard deviation of $W = 2 X - 18$ .mean $94$ , SD $22$ $X$ has mean 14 and standard deviation 6. Find the mean and standard deviation of $W = - 3 X - 4$ .mean $- 46$ , SD $18$ $X$ has mean 37 and standard deviation 8; $Y$ has mean 8 and standard deviation 15, and they are independent. Find the mean and standard deviation of $X - Y$ .mean $29$ , SD $17$ $X$ has mean 40 and standard deviation 4; $Y$ has mean 31 and standard deviation 7, and they are independent. Find the mean and standard deviation of $X - Y$ , the standard deviation to the nearest hundredth.mean $9$ , SD $8.06$ $X$ has mean 23 and standard deviation 10. Find the mean and standard deviation of $W = 5 X + 23$ .mean $138$ , SD $50$ $X$ has mean 53 and standard deviation 3; $Y$ has mean 13 and standard deviation 4, and they are independent. Find the mean and standard deviation of $X + Y$ .mean $66$ , SD $5$ $X$ has mean 52 and standard deviation 7. Find the mean and standard deviation of $W = - 2 X - 17$ .mean $- 121$ , SD $14$ $X$ has mean 18 and standard deviation 2; $Y$ has mean 13 and standard deviation 3, and they are independent. Find the mean and standard deviation of $X + Y$ , the standard deviation to the nearest hundredth.mean $31$ , SD $3.61$ $X$ has mean 50 and standard deviation 5. Find the mean and standard deviation of $W = 5 X - 12$ .mean $238$ , SD $25$ $X$ has mean 5 and standard deviation 8. Find the mean and standard deviation of $W = - 5 X + 30$ .mean $5$ , SD $40$ $X$ has mean 14 and standard deviation 3. Find the mean and standard deviation of $W = - 3 X + 14$ .mean $- 28$ , SD $9$ $X$ has mean 41 and standard deviation 7. Find the mean and standard deviation of $W = - 2 X - 1$ .mean $- 83$ , SD $14$ $X$ has mean 27 and standard deviation 6. Find the mean and standard deviation of $W = 2 X + 26$ .mean $80$ , SD $12$ $X$ has mean 47 and standard deviation 4; $Y$ has mean 18 and standard deviation 7, and they are independent. Find the mean and standard deviation of $X + Y$ , the standard deviation to the nearest hundredth.mean $65$ , SD $8.06$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Combining Random VariablesAnswer keyVersion 1

Date Period

Answer each question.

$X$ has mean 20 and standard deviation 8. Find the mean and standard deviation of $W = 3 X + 30$ .mean $90$ , SD $24$
$X$ has mean 34 and standard deviation 3; $Y$ has mean 8 and standard deviation 4, and they are independent. Find the mean and standard deviation of $X + Y$ .mean $42$ , SD $5$
$X$ has mean 24 and standard deviation 2; $Y$ has mean 13 and standard deviation 3, and they are independent. Find the mean and standard deviation of $X - Y$ , the standard deviation to the nearest hundredth.mean $11$ , SD $3.61$
$X$ has mean 15 and standard deviation 9. Find the mean and standard deviation of $W = - 5 X + 30$ .mean $- 45$ , SD $45$
$X$ has mean 17 and standard deviation 2; $Y$ has mean 19 and standard deviation 3, and they are independent. Find the mean and standard deviation of $X + Y$ , the standard deviation to the nearest hundredth.mean $36$ , SD $3.61$
$X$ has mean 23 and standard deviation 3; $Y$ has mean 7 and standard deviation 4, and they are independent. Find the mean and standard deviation of $X - Y$ .mean $16$ , SD $5$
$X$ has mean 56 and standard deviation 11. Find the mean and standard deviation of $W = 2 X - 18$ .mean $94$ , SD $22$
$X$ has mean 14 and standard deviation 6. Find the mean and standard deviation of $W = - 3 X - 4$ .mean $- 46$ , SD $18$
$X$ has mean 37 and standard deviation 8; $Y$ has mean 8 and standard deviation 15, and they are independent. Find the mean and standard deviation of $X - Y$ .mean $29$ , SD $17$
$X$ has mean 40 and standard deviation 4; $Y$ has mean 31 and standard deviation 7, and they are independent. Find the mean and standard deviation of $X - Y$ , the standard deviation to the nearest hundredth.mean $9$ , SD $8.06$
$X$ has mean 23 and standard deviation 10. Find the mean and standard deviation of $W = 5 X + 23$ .mean $138$ , SD $50$
$X$ has mean 53 and standard deviation 3; $Y$ has mean 13 and standard deviation 4, and they are independent. Find the mean and standard deviation of $X + Y$ .mean $66$ , SD $5$
$X$ has mean 52 and standard deviation 7. Find the mean and standard deviation of $W = - 2 X - 17$ .mean $- 121$ , SD $14$
$X$ has mean 18 and standard deviation 2; $Y$ has mean 13 and standard deviation 3, and they are independent. Find the mean and standard deviation of $X + Y$ , the standard deviation to the nearest hundredth.mean $31$ , SD $3.61$
$X$ has mean 50 and standard deviation 5. Find the mean and standard deviation of $W = 5 X - 12$ .mean $238$ , SD $25$
$X$ has mean 5 and standard deviation 8. Find the mean and standard deviation of $W = - 5 X + 30$ .mean $5$ , SD $40$
$X$ has mean 14 and standard deviation 3. Find the mean and standard deviation of $W = - 3 X + 14$ .mean $- 28$ , SD $9$
$X$ has mean 41 and standard deviation 7. Find the mean and standard deviation of $W = - 2 X - 1$ .mean $- 83$ , SD $14$
$X$ has mean 27 and standard deviation 6. Find the mean and standard deviation of $W = 2 X + 26$ .mean $80$ , SD $12$
$X$ has mean 47 and standard deviation 4; $Y$ has mean 18 and standard deviation 7, and they are independent. Find the mean and standard deviation of $X + Y$ , the standard deviation to the nearest hundredth.mean $65$ , SD $8.06$

How to do these

X has mean 10 and SD 3; Y has mean 6 and SD 4, and they are independent. Find the mean and SD of $X - Y$

Means subtract: 10 - 6.
Variances add, even for a difference: 9 + 16 = 25.
The SD is the square root.

The answer is mean $4$ , SD $5$ .

Where students go wrong

Subtracting the standard deviations for X - Y. Spread never cancels: the variances add.

Also called linear combinations of random variables, sum of random variables or difference of random variables.

Questions about these worksheets

Yes. Every combining random variables sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Statistics is usually taken around 11th or 12th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the combining random variables questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

Subtracting the standard deviations for X - Y. Spread never cancels: the variances add.

Combining random variables worksheet

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How to do these

Where students go wrong

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