ap stats study guides

โœŒ๏ธย  Unit 2 - Exploring Two-Variable Data

โš–๏ธย  Unit 6 - Inference for Categorical Data: Proportions

๐Ÿ˜ผย  Unit 7 - Inference for Qualitative Data: Means

โœณ๏ธย  Unit 8 Inference for Categorical Data: Chi-Square

๐Ÿ“ˆย  Unit 9 - Inference for Quantitative Data: Slopes

๐Ÿงย  Multiple Choice Questions (MCQs)

4.9 Combining Random Variables

#exploringdata

#anticipatingpatterns

โฑ๏ธย ย 2 min read

written by

kanya shah


This section is about transforming random variables by adding/subtracting or multiplying/dividing by a constant. Make sure you know how to combine random variables to calculate and interpret the mean and standard deviation.

Linear Transformations of a Random Variable

Y = a + BX

Adding/Subtracting by a constant affects measures of center and location but does NOT affect variability or the shape of a distribution. Multiplying or dividing by a constant affects center, location, and variability measures but wonโ€™t change the shape of a distribution.ย 

How to Find the Expected Value of the Sum/Difference of Two Random Variables

Sum: For any two random variables X and Y, if S = X + Y, the mean of S is meanS= meanX + meanY. Put simply, the mean of the sum of two random variables is equal to the sum of their means.ย 

Difference: For any two random variables X and Y, if D = X - Y, the mean of D is meanD= meanX - meanY. The mean of the difference of two random variables is equal to the difference of their means. The order of subtraction is important.ย 

Independent Random Variables: If knowing the value of X does not help us predict the value of X, then X and Y are independent random variables.ย 

Standard Deviation of the Sum/Difference of Two Independent Random Variables

Sum: For any two independent random variables X and Y, if S = X + Y, the variance of S is SD^2= (X+Y)^2 . To find the standard deviation, take the square root of the variance formula: SD = sqrt(SDX^2 + SDY^2).ย 

Standard deviations do not add; use the formula or your calculator.ย 

Difference: For any two independent random variables X and Y, if D = X - Y, the variance of D is D^2= (X-Y)^2=x2+Y2. To find the standard deviation, take the square root of the variance formula: D=sqrt(x2+Y2). Notice that you are NOT subtracting the variances (or the standard deviation in the latter formula).ย 

๐ŸŽฅWatch: AP Stats - Combining Random Variables

continue learning

Slide 1 of 13
Fiveable

Join Our Community

Fiveable Community students are already meeting new friends, starting study groups, and sharing tons of opportunities for other high schoolers. Soon the Fiveable Community will be on a totally new platform where you can share, save, and organize your learning links and lead study groups among other students!๐ŸŽ‰

Fiveable Logo

2550 north lake drive
suite 2
milwaukee, wi 53211

92% of Fiveable students earned a 3 or higher on their 2020 AP Exams.

*apยฎ and advanced placementยฎ are registered trademarks of the college board, which was not involved in the production of, and does not endorse, this product.

ยฉ fiveable 2020 | all rights reserved.