document.write( "Question 367420: show me how to found the mean and standard deviation of four-digit uniformly distributed lottery numbers (0000 - 9999) \n" ); document.write( "

Algebra.Com's Answer #261912 by robertb(5830) $\"\"$ $\"About$

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For each four-digit number x, p(x) = $\"1%2F10%5E4+=+1%2F10000\"$ . The mean:
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+...+
\n" ); document.write( " $\"%281%2F10000%29%2A%289998%29+%2B+%281%2F10000%29%2A%289999%29\"$
\n" ); document.write( "=(1/10000)*(sum of integers from 1 to 9999)
\n" ); document.write( "= $\"%281%2F10000%29%2A%28%28%289999%29%2A%2810000%29%29%2F2%29+=+9999%2F2=4999.5\"$ .
\n" ); document.write( "The variance is given by
\n" ); document.write( " $\"Var%28X%29+=+E%28X%5E2%29+-+%28E%28X%29%29%5E2\"$
\n" ); document.write( "= $\"%281%2F10000%29%2A%28%28%289999%29%2A%2810000%29%2A%2819999%29%29%2F6%29-%289999%2F2%29%5E2\"$
\n" ); document.write( "= $\"%28%289999%29%2A%2819999%29%29%2F6+-+%289999%2F2%29%5E2\"$
\n" ); document.write( "= $\"%289999%2F2%29%2A%2819999%2F3+-+9999%2F2%29\"$
\n" ); document.write( "= $\"%289999%2F2%29%2A%2810001%2F6%29\"$
\n" ); document.write( "= $\"%28%283333%29%2A%2810001%29%29%2F4\"$ .
\n" ); document.write( "The standard deviation would be the square root of this. \n" ); document.write( "

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