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CMA Foundation · Fundamentals of Business Mathematics and Statistics · Probability

The probability distribution of a random variable X is: X = 1, 2, 3, 4 with P = 0.1, 0.3, 0.4, 0.2. Find the variance of X.

The variance is 0.81. The mean is 2.7 and the mean of squares is 8.1, so variance equals 8.1 minus 7.29, which is 0.81. Using the formula E(X²) minus the square of E(X) avoids needing deviations from the mean.

  1. A0.81Correct
  2. B0.89
  3. C0.85
  4. D0.93

Explanation

E(X) = 0.1+0.6+1.2+0.8 = 2.7. E(X²) = 0.1+1.2+3.6+3.2 = 8.1. Variance = 8.1 - 2.7² = 8.1 - 7.29 = 0.81. The option 0.89 results from an arithmetic slip in the squares.

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