Discussion
For which distribution mean and variance are equal ?
Answer: C
Mean and variance are equal for the Poisson distribution.
For a Poisson distribution with parameter \(\lambda\), the probability of k events is \(P(k) = e^{-\lambda}\lambda^{k}/k!\), and both the mean and the variance equal \(\lambda\). This is why it describes counts of rare, random events, such as mutations per generation or colonies per plate.
For a binomial distribution the mean is np and the variance npq, which is smaller than the mean because q is less than 1. A chi-square distribution with n degrees of freedom has mean n and variance 2n. A normal distribution has two independent parameters, the mean and the variance, which need not be equal.
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