CK-12 Probability and Statistics - Advanced

7.5. Sums and Differences of Independent Random Variables http://www.ck12.org

σ^225 y− 20 x=σ^225 y+σ^220 x= ( 27. 75 )^2 +( 16. 62 )^2 = 1046. 2896

σ 25 y− 20 x≈$32. 35

Lesson Summary

A chance process can be displayed as a probability distribution that describes all the possible outcomes,x. You can
also determine the probability of any set of possible outcomes. A probability distribution table for a random variable,
x, consists of two columns in which all of the outcomes are listed in one column and all of the associated probability
in the other. The expected value and the variance of a probability distribution can be calculated using the formulas:

E(X) =μx=∑xipi

Var(X) =σ^2 x=∑(xi−μx)^2 pi

For random variablesXandYand constantscandd, the mean and the standard deviation of a linear transformation
are given by:

μc+dx=c+dμx

σc+dx=

∣

∣d

∣

∣σx

If the random variablesXandYare added or subtracted, the mean is calculated by:

μX+Y=μX+μY

μX−Y=μX−μY

IfXandYare independent, then the variance is computed by:

σ^2 X+Y=σ^2 X+σ^2 Y

σ^2 X−Y=σ^2 X+σ^2 Y

Points to Consider

• Are these concepts applicable to real-life situations?


• Will knowing these concepts allow you estimate information about a population?

Review Questions

1. It is estimated that 70% of the students attending a school in a rural area, take the bus to school. Suppose
   you randomly select three students from the population. Construct the probability distribution of the random