Today Today: More Chapter 3 Reading: –Please read Chapter 3 –Suggested Problems: 3.2, 3.9, 3.12, 3.20, 3.23, 3.24, 3R5, 3R9

Example: Lifetime of 2 types of car (100 cars of each brand)... which would you buy?

Variability The mean of a random variable does not tell the entire story about distribution The variability in terms of average deviation from the mean is frequently of interest How can we measure the typical distance between the values of X and the mean?

Mean Deiviation Properties:

Variance Properties:

Variance Properties:

Standard Deviation Properties:

Standard Deviation Properties:

Example What is the variance and standard deviation for each brand in the car example?

Covariance and Correlation Summarized relationship between two variables using their joint distribution Can measure their joint variability using the covariance:

Covariance and Correlation Properties:

Covariance and Correlation Correlation coefficient: