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MHT CET202615 April 2026Evening ShiftMathematicsProbabilityActual

For the following probability distribution, the standard deviation of the random variable X is X 2 3 4 p(X= x ) 0.2 0.5 0.3

Options

  1. A0.5
  2. B0.6
  3. C0.61
  4. D0.7

Correct answer

D. 0.7

Step-by-step solution

E(X) = x_i p_i = 2(0.2) + 3(0.5) + 4(0.3) E(X) = 0.4 + 1.5 + 1.2 = 3.1 E(X^2) = x_i^2 p_i = 4(0.2) + 9(0.5) + 16(0.3) E(X^2) = 0.8 + 4.5 + 4.8 = 10.1 Var (X) = E(X^2) - (E(X))^2 Var (X) = 10.1 - (3.1)^2 = 10.1 - 9.61 = 0.49 Standard deviation = Var (X) = 0.49 = 0.7 Answer: 0.7

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