TITLE: Expected number of (0,1) distributed continuous random variables required to sum upto 1
QUESTION [7 upvotes]: I define $X_i$ as a random variable that is uniformly distributed between (0,1). What is the expected number of such variables I require to make the sum go just higher than 1. 
Thanks

REPLY [5 votes]: This problem is well-known. For an answer, see, for example, the first part of Section 2 in http://myweb.facstaff.wwu.edu/curgus/Papers/27Unexpected.pdf, or Equations (7)-(10) in http://mathworld.wolfram.com/UniformSumDistribution.html