An unexpected limit of expected values
نویسندگان
چکیده
Let t 0. Select numbers randomly from the interval [0, 1] until the sum is greater than t. Let (t) be the expected number of selections. We prove that (t) = et for 0 t 1. Moreover, limt→+∞ ( (t)− 2t)= 3 . This limit is a special case of our asymptotic results for solutions of the delay differential equation f ′(t) = f (t) − f (t − 1) for t > 1. We also consider four other solutions of this equation that are related to the above selection process. 2006 Elsevier GmbH. All rights reserved. MSC 2000: Primary 34K06; 60G50; 34K60
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