Combining Random Variables

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Presentation transcript:

Combining Random Variables

Combining Random Variables Example: Jim and Bob go bowling. Suppose their scores are normally distributed with the following: AVERAGE St. Dev. Jim 163 12 Bob 201 17

Example: AVERAGE St. Dev. Jim 163 12 Bob 201 17 What is the mean and standard deviation of the SUM of their scores?

Rule for sum/difference: The mean of the sum (or difference) of random variables is the sum (or difference) of the means. For our example:

Example: AVERAGE St. Dev. Jim 163 12 Bob 201 17 What is the mean of their combined score?

Example: AVERAGE St. Dev. Jim 163 12 Bob 201 17 What is the mean difference in their scores?

Rule for Standard Deviation The variance of the sum of random variables is the sum of the variances. ** You must ADD VARIANCES, not standard deviations.

Example: AVERAGE St. Dev. Jim 163 12 Bob 201 17 What is the standard deviation of their combined score? - First find the variance:

Example Cont. So the variance of the sum is: (12)2 + (17)2 = 433 (12)2 + (17)2 = 433 Then, the standard deviation is: NOTE – THIS IS NOT THE SUM OF THE STANDARD DEVIATIONS!!

Example: AVERAGE St. Dev. Jim 163 12 Bob 201 17 What is the standard deviation of the difference of their scores? NOTE: We still ADD VARIANCES!

Think about… Why do we ADD variances for the difference of two variables???????