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Conference rusure::math

Title:Mathematics at DEC
Moderator:RUSURE::EDP
Created:Mon Feb 03 1986
Last Modified:Fri Jun 06 1997
Last Successful Update:Fri Jun 06 1997
Number of topics:2083
Total number of notes:14613

641.0. "What's average number of flips to get heads ?" by VIDEO::OSMAN (and silos to fill before I feep, and silos to fill before I feep) Mon Jan 05 1987 18:17

An easier coin-flipping problem:

	Flip a fair coin until you get heads.  What's the average number
	of times you have to flip ?

/Eric
T.RTitleUserPersonal
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641.12COMET::ROBERTSDwayne RobertsMon Jan 05 1987 21:307
    
    (1/2)*1 + (1/4)*2 + (1/8)*3 + (1/16)*4 + ... + (2^-i)*i + ...
    
    = (1/2)/((1-1/2)^2)
    
    = 2
    
641.2a more general solutionESTORE::ROOSThu Jan 15 1987 18:3124
    
    
    I agree wih the solution of:
    
    (1/2)*1 + (1/4)*2 + (1/8)*3 + ... + (2^-i)*i + ...
    
    The sum does approach 2.
    
    As a matter of fact the sum of the first i terms = 2 - ((i + 2)/(2^i))
    
    Thus, as i becomes large ((i + 2)/(2^i)) converges to zero
    
    and the sum converges to 2.
    
    Got any more interesting problems!!!  The one in Note 622 looks
    nice.
    
    
    
    
    Note:  first two terms add to 1
           starting with the 3 rd term