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Choose a random number between $0$ and $1$ and record its value. Do this again and add the second number to the first number. Keep doing this until the sum of the numbers exceeds $1$. What's the expected value of the number of random numbers needed to accomplish this?

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    See http://mathworld.wolfram.com/UniformSumDistribution.html Scroll down until you hit the reference to Derbyshire2012-02-20
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    I am flummoxed, based on the comments of the OP to all the attempted solutions. How can you even talk about this without the idea of expected value? How can you discuss a uniform distribution without first knowing integration?2018-08-11

3 Answers 3