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CA Foundation · Quantitative Aptitude · Theoretical Distributions

Which one of the following statements about the binomial distribution with parameters n and p (0 < p < 1) and the Poisson distribution with parameter m is correct?

The binomial has variance npq, which is less than its mean np because q is below 1, while the Poisson has variance equal to its mean m. So only the Poisson has mean equal to variance.

  1. ABoth distributions always have mean equal to variance
  2. BThe binomial has variance less than its mean, while the Poisson has variance equal to its meanCorrect
  3. CThe binomial has variance greater than its mean, while the Poisson has variance equal to its mean
  4. DBoth distributions have variance less than the mean

Explanation

For the binomial, mean = np and variance = npq, and since q < 1 the variance is less than the mean. For the Poisson, mean = variance = m. Option 1 is wrong because only the Poisson has equal mean and variance.

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