Skip to content

CA Foundation · Quantitative Aptitude · Theoretical Distributions

For a binomial random variable with n = 10 trials and success probability p = 0.3, which pair gives its mean and variance?

The mean is 3 and the variance is 2.1. For a binomial distribution the mean is np, which is 10 times 0.3, and the variance is npq, which is 10 times 0.3 times 0.7. Mean and variance are therefore 3 and 2.1.

  1. AMean 3, variance 2.1Correct
  2. BMean 3, variance 0.9
  3. CMean 7, variance 2.1
  4. DMean 2.1, variance 3

Explanation

Mean = np = 10 × 0.3 = 3. Variance = npq = 10 × 0.3 × 0.7 = 2.1. Variance 0.9 results from using p² (0.3 × 3) rather than q = 0.7, and mean 7 uses the failure probability.

Did you get it right without looking?

One question tells you little. A timed set on Theoretical Distributions shows your real accuracy, how long you take and where you lose marks.

Practise Theoretical DistributionsFree diagnostic mock

More Theoretical Distributions questions