Calculate the arithmetic mean
Probability
Level
3
If I generate N random numbers between 0 and 1 what is the Arithmetic mean of all the generated numbers as N→ ∞. You can assume that the generated random numbers are uniformly distributed.
0.7
0.5
1
0.36
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1 solution
Due to the random numbers being perfectly normally distributed and as N tends to infinity the numbers generated can be considered as 0, 1/N,2/N,3/N,4/N......N-2/N,1 The arithmetic mean of these N numbers would be ((N-2)*(N-1)/2N + 1)/N. Under limits as N → ∞ the arithmetic mean can be approximated to 0.5.