SOLUTION: show me how to found the mean and standard deviation of four-digit uniformly distributed lottery numbers (0000 - 9999)

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Question 367420: show me how to found the mean and standard deviation of four-digit uniformly distributed lottery numbers (0000 - 9999)
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
For each four-digit number x, p(x) = 1%2F10%5E4+=+1%2F10000. The mean:
+...+
%281%2F10000%29%2A%289998%29+%2B+%281%2F10000%29%2A%289999%29
=(1/10000)*(sum of integers from 1 to 9999)
= %281%2F10000%29%2A%28%28%289999%29%2A%2810000%29%29%2F2%29+=+9999%2F2=4999.5.
The variance is given by
Var%28X%29+=+E%28X%5E2%29+-+%28E%28X%29%29%5E2
=%281%2F10000%29%2A%28%28%289999%29%2A%2810000%29%2A%2819999%29%29%2F6%29-%289999%2F2%29%5E2
=%28%289999%29%2A%2819999%29%29%2F6+-+%289999%2F2%29%5E2
=%289999%2F2%29%2A%2819999%2F3+-+9999%2F2%29
=%289999%2F2%29%2A%2810001%2F6%29
=%28%283333%29%2A%2810001%29%29%2F4.
The standard deviation would be the square root of this.