The following two statements relate to probability distributions. Choose the correct code for the statements being correct or incorrect.

Statement I: When ‘p' and 'q' are equal in the binomial distribution, the shape of the distribution is perfectly symmetrical irrespective of the size of 'n'.

Statement II: The mean and the variance of Poisson distribution are not equal.

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  1. Statement I is correct, but II is incorrect.
  2. Statement II is correct, but I is incorrect.
  3. Both the statements I and II are correct.
  4. Both the statements I and II are incorrect.

Answer (Detailed Solution Below)

Option 4 : Both the statements I and II are incorrect.
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Detailed Solution

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The correct answer is Both the statements I and II are incorrect.

Key PointsStatement I: When ‘p' and 'q' are equal in the binomial distribution, the shape of the distribution is perfectly symmetrical irrespective of the size of 'n'.

This statement is incorrect. In the binomial distribution, 'p' represents the probability of success on a single trial, 'q' represents the probability of failure (1 - p), and 'n' represents the number of trials. The shape of the binomial distribution is not perfectly symmetrical when 'p' and 'q' are equal, regardless of the size of 'n'. The symmetry of the binomial distribution depends on the value of 'p' and 'q' relative to 0.5, as well as the size of 'n'.

Statement II: The mean and the variance of Poisson distribution are not equal.

The mean and the variance of a Poisson distribution are equal. In a Poisson distribution, both the mean (λ) and the variance (σ^2) are equal to the parameter λ, which represents the average rate of occurrence of an event. 

Hence the correct answer is Both the statements I and II are incorrect.

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