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Roll in MATLAB 500 times threesome-dice (3 dice) and sum them.Find in addition:

  • max and min in each sequence
  • mean values of sum/min/max.
  • deviations of sum/min/max.
  • correlation coefficients between sum/min/max.

Explain the numbers (e.g the relative size of deviations and between which couples correlation coefficients are smaller).

I managed to do a-d but I'm stuck in e. the correlation between the sum and max (same for min) is around $0.75$ and between the min-max is only $0.29$.The standard deviations are as following:

  • between max to the min is 1.1855
  • between sum to the min is 1.2327
  • between sum to the max is 0.9756

How can I explain these results?

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1 Answer 1

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This is not a proof, nor is it complete, but here is some intuition.

the correlation between the sum and max (same for min) is around 0.75 and between the min-max is only 0.29

Because the problem is symmetrical (around 3.5) the theoretical correlation between the min and the sum, and the max and the sum is exactly the same.

The die that makes up the max (same for min) will always be included in the calculation of the sum. However, the max and min wil usually be determined by completely different dies. Therefore the correlation between max (or min) and sum would intuitively be stronger than the correlation between max and min.

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