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?
Choose a random number between $0$ and $1$ and record its value. Keep doing it until the sum of the numbers exceeds $1$. How many tries do we need?
36
$\begingroup$
probability
probability-theory
expectation
-
5See http://mathworld.wolfram.com/UniformSumDistribution.html Scroll down until you hit the reference to Derbyshire – 2012-02-20
-
0I 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