The variable X takes two values x1 and x2 with frequencies f1 and f2 respectively. If σ denotes the standard deviation of X, then σ2=

The variable X takes two values x1 and x2 with frequencies f1 and f2 respectively. If σ denotes the standard deviation of X, then σ2=

  1. A

    f12x12+f22x22f1+f2f1x1+f2x2f1+f22

  2. B

    f1f2f1+f22x1x22

  3. C

    f1f2f1f22x1x22

  4. D

    none of these

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    Solution:

    We have,

      σ2=f1x12+f2x22f1+f2f1x1+f2x2f1+f22

    σ2=1f1+f22f12x12+f22x22+f1f2x12+x22f12x12f22x222f1f2x1x2σ2=f1f2f1+f22x1x22

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