In ______ distribution, mean = variance.(a) Normal(b) Binomial(c) Poisson(d) none of these

Break Down the Problem

1. Identify the key point of the question: the type of distribution where the mean equals the variance.
2. Evaluate each option provided.

Relevant Concepts

1. Normal Distribution: In a normal distribution, the mean and variance are related, but they are not equal.
2. Binomial Distribution: In a binomial distribution, the mean is given by $np$ and the variance by $np(1-p)$; they are not equal.
3. Poisson Distribution: In a Poisson distribution, the mean $\lambda$ is equal to the variance $\lambda$.

Analysis and Detail

1. Normal distribution does not have mean equal to variance.
2. Binomial distribution has different forms for mean and variance.
3. Poisson distribution is characterized by having the mean equal to the variance.

Verify and Summarize

Upon evaluating each of the options, it is clear that the Poisson distribution is the only one where the mean equals the variance.

Final Answer

The correct answer is (c) Poisson.