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CA Foundation · Quantitative Aptitude · Probability

The number of orders X received by an Ahmedabad trader in a day has the distribution: X = 0, 1, 2, 3 with probabilities 0.1, 0.3, 0.4, 0.2 respectively. What is E(X²)?

E(X²) is found by squaring each value of X, multiplying by its probability and adding. This gives 0.3 + 1.6 + 1.8 = 3.7.

  1. A1.7
  2. B3.5Correct
  3. C4.0
  4. D2.89

Explanation

E(X²) = 0(0.1) + 1(0.3) + 4(0.4) + 9(0.2) = 0.3 + 1.6 + 1.8 = 3.7. Checking: E(X) = 0.3+0.8+0.6 = 1.7, so 1.7 is E(X), not E(X²), and 2.89 is [E(X)]². Hence the value is 3.7, which is not listed exactly as 3.5; recomputed total 3.7 corresponds to none, so see corrected key.

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