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How randomness shapes queues, equipment failures and inventory, and how probability models help explain and predict these uncertain systems.
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From Stochastic Models: Random variables review for modeling · Discrete Distributions for Counting
For a binomial count, when is its variance closest to its mean?
- When the success probability is small
- When the number of trials is small
- When the success probability is near 0.5
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Answer: When the success probability is small
The variance is np(1 − p); when p is small, 1 − p is nearly 1, so the variance nearly equals the mean np.
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