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CA Foundation · Quantitative Aptitude · Theoretical Distributions

Consider three distributions: (I) Binomial with n = 20, p = 0.5; (II) Poisson with mean 10; (III) Normal with mean 10 and variance 5. Which statement is correct?

Distributions I and III have identical mean 10 and variance 5. The binomial has mean 20 × 0.5 = 10 and variance 20 × 0.5 × 0.5 = 5, while the Poisson has variance equal to its mean, 10, so it differs.

  1. AI and II have the same mean and the same variance
  2. BI and III have the same mean and the same varianceCorrect
  3. CII and III have the same mean and the same variance
  4. DAll three have the same mean and the same variance

Explanation

I: mean = np = 10, variance = npq = 20 × 0.5 × 0.5 = 5. II: mean 10, variance 10. III: mean 10, variance 5. So I and III match on both. I and II differ in variance (5 versus 10), and II and III also differ in variance.

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