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Find the mean (expected value) and the standard deviation for the distribution of the difference (absolute value) of two dice .???

 Mar 19, 2019
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1) for each possible roll of 2 dice determine the absolute difference

 

2) for each value generated in (1) count the number of times it occurs.  Divide this count by 36.

This is the probability that this absolute difference occurs.

 

3) What you now have is a distribution on the absolute difference

 

4) multiply each value by it's probability and sum up the results.  This is the mean value.

 

5) multiply each value squared by it's probability and sum the results.  The is the expected value of of the absolute difference squared.

 

6) Find the variance as The number you found in (5) minus the number you found in (4) squared.

i.e. var = E[|roll diff|2] - (E[|roll diff|])2 

 

7) standard deviation is the square root of variance

 Mar 19, 2019

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