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I recently got a tute question which I don't know how to proceed with and I believe that the tutor won't provide solution... The question is

Pick a real number randomly (according to the uniform measure) in the interval $[0, 2]$. Do this one million times and let $S$ be the sum of all the numbers. What, approximately, is the probability that
a) $S\ge1,$
b) $S\ge0.001,$
c) $S\ge0$?
Express as a definite integral of the function $e^\frac{-x^2}{2}$.

Can anyone show me how to do it? It is in fact from a Fourier analysis course but I guess I need some basic result from statistcs which I am not familiar with at all..

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    (c) is easy and has nothing to do with the function $e^\frac{−x^2}{2}$.2012-08-19
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    Since you are summing 1,000,000 random numbers with mean value 1, the sum will be usually about 1,000,000. If you are asking about the average value of the 1,000,000 numbers, it becomes more interesting.2012-08-19
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    @marty: not much: (a) would become $\frac12$, (c) would still be $1$ and (b) would still be very close to $1$2012-08-19

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