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Manipal MET2014MathematicsStatistics

The variance of first n natural numbers is

Options

  1. An(n+1) 12
  2. B(n+1)(n+5) 12
  3. C(n+1)(n-5) 12
  4. Dn(n-5) 12

Correct answer

C. (n+1)(n-5) 12

Step-by-step solution

Variance of first n natural numbers is given by aligned Variance & = n^2 n - ( n n )^2 & = n(n+1)(2 n-1) 6 n - ( n(n+1) 2 n )^2 & =(n+1) [ 2 n-1 6 - (n+1) 4 ] & = (n+1) 12 [4 n-2-3 n-3] & = (n+1) 12 (n-5) aligned

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