How to differentiate between binomial and Poisson distributions effectively

How to differentiate between binomial and Poisson distributions effectively

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Frequently Asked Questions

The Binomial distribution models the number of successes in a fixed number of independent trials, while the Poisson distribution models the number of events occurring in a fixed interval of time or space. Binomial has a fixed number of trials (n), Poisson does not.
Look for keywords like fixed number of trials (Binomial) versus events occurring per unit of time/space (Poisson). Also, consider if theres a clear probability of success for each trial (Binomial).
There must be a fixed number of trials (n), each trial must be independent, there are only two possible outcomes (success or failure), and the probability of success (p) must be constant for each trial.
Events must occur randomly and independently, and the average rate of events (λ) must be constant over the interval.
For a Binomial distribution, the variance is np(1-p). For a Poisson distribution, the variance is equal to its mean (λ).
Yes, when the number of trials (n) is large and the probability of success (p) is small, such that np (which equals λ) is a constant, then Poisson can approximate Binomial.
Binomial: The number of heads when flipping a coin a certain number of times. Poisson: The number of customers arriving at a store in an hour.
For Binomial, use the formula P(X = k) = (n choose k) * p^k * (1-p)^(n-k). For Poisson, use the formula P(X = k) = (e^-λ * λ^k) / k!, where k is the number of events.
Confusing the conditions for each distribution, incorrectly identifying n and p in Binomial problems, and not checking if the rate (λ) is constant in Poisson problems. Also, remember to use the correct formula for calculating probabilities.