Discussion
Which of the following distribution has, mean = variance ?
Answer: B
The distribution with mean equal to variance is the Poisson.
A Poisson distribution with parameter \(\lambda\) has mean \(\lambda\) and variance \(\lambda\), which is used as a quick check on whether count data (accidents, colonies on a plate, defects) follow it.
The binomial has mean \(np\) and variance \(npq\), which is always smaller than the mean because \(q \lt 1\). In the normal distribution the mean \(\mu\) and variance \(\sigma^{2}\) are independent parameters. A chi-square distribution with \(k\) degrees of freedom has mean \(k\) and variance \(2k\).
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