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December 9th, 2009, 04:18 PM   #1
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expectation and Dice Probability Problem

Here is another question that I have been stuck on.

Suppose we roll 6 fair dice, and let X be the maximum number we roll. Compute E(x).

So we have to find the expected maximum value.
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December 9th, 2009, 05:12 PM   #2
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Re: expectation and Dice Probability Problem

Hi;

Could you clarify your question for me?

For instance I throw these six die

1,5,5,6,2,4 the maximum value is 6 or the sum is 23, which do you want the expected value of.

Thanks!
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December 9th, 2009, 05:37 PM   #3
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Re: expectation and Dice Probability Problem

The maximum number was 6. We want to find the expected max if you throw 6 dice. I think I might have figured it out. I got

Expected Max= (1-(5/6)^6)+(1-(4/6)^6)+...+(1-(1/6)^6)
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December 9th, 2009, 07:31 PM   #4
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Re: expectation and Dice Probability Problem

you are missing a term of (1-(0/6)^6) in the sum.
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December 9th, 2009, 11:01 PM   #5
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Re: expectation and Dice Probability Problem

you right, thank you for the help.
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December 19th, 2009, 01:53 PM   #6
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Re: expectation and Dice Probability Problem

Helo everyone, I am new here. Is this answer really correct?
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December 19th, 2009, 03:20 PM   #7
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Re: expectation and Dice Probability Problem

Hi;

Expected Max= (1-(5/6)^6)+(1-(4/6)^6)+...+(1-(0/6)^6) = 259421 / 46656

This is correct, I have verified by actually counting the max of all 6^6 ways you can throw 6 die by computer. The answer I got was the same.
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