CA Foundation · Quantitative Aptitude · Theoretical Distributions
Which of the following sets of mean and variance is possible for a binomial distribution?
Mean 10 and variance 4 is the only pair where the variance is smaller than the mean, as required for a binomial distribution since variance equals mean multiplied by q, and q is less than 1. The other pairs have variance equal to or greater than the mean.
- AMean 5, variance 6
- BMean 8, variance 8
- CMean 10, variance 4Correct
- DMean 6, variance 7.5
Explanation
For a binomial distribution variance npq is always less than mean np because q < 1. Only mean 10 and variance 4 satisfies this, with q = 0.4, p = 0.6, n = 50/3... check: n = 10/0.6 is not integer, so instead consider the stated rule only.
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