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KCET2024MathematicsProbability

A random variable X has the following probability distribution: If the mean of the random variable X is 1 / 3 , then the variance is

Options

  1. A1 18
  2. B5 18
  3. C7 18
  4. D11 18

Correct answer

B. 5 18

Step-by-step solution

Mean = _ i=1 ^n x_i P (x_i ) 1 3 =0 25 36 +1 k+2 1 36 1 3 =k+ 1 18 k= 1 3 - 1 18 = 6-1 18 = 5 18 Now, variance = _ i=0 ^n x_i^2 P_i(x)-( mean )^2=(0)^2 25 36 +(1)^2 k+(2)^2 1 36 - 1 9 =0+k+ 1 9 - 1 9 =k= 5 18 Hence, variance = 5 18

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