My Math Forum expectation and Dice Probability Problem

 December 9th, 2009, 04:18 PM #1 Newbie   Joined: Dec 2009 Posts: 9 Thanks: 0 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.
 December 9th, 2009, 05:12 PM #2 Senior Member   Joined: Dec 2009 From: Las Vegas Posts: 209 Thanks: 0 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!
 December 9th, 2009, 05:37 PM #3 Newbie   Joined: Dec 2009 Posts: 9 Thanks: 0 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)
 December 9th, 2009, 07:31 PM #4 Member   Joined: Oct 2009 Posts: 64 Thanks: 0 Re: expectation and Dice Probability Problem you are missing a term of (1-(0/6)^6) in the sum.
 December 9th, 2009, 11:01 PM #5 Newbie   Joined: Dec 2009 Posts: 9 Thanks: 0 Re: expectation and Dice Probability Problem you right, thank you for the help.
 December 19th, 2009, 01:53 PM #6 Newbie   Joined: Dec 2009 Posts: 1 Thanks: 0 Re: expectation and Dice Probability Problem Helo everyone, I am new here. Is this answer really correct?
 December 19th, 2009, 03:20 PM #7 Senior Member   Joined: Dec 2009 From: Las Vegas Posts: 209 Thanks: 0 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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