Question

In Python 3, for the approximation of binomial by Poisson distribution, consider the case when the probability p of success in a Bernoulli trial is small. What is the result?

a) The binomial distribution is always preferred.
b) The Poisson distribution is always preferred.
c) Both distributions provide similar results.
d) It depends on the value of p.

Answer 1

When the probability p of success in a Bernoulli trial is small, the Poisson distribution is often preferred to approximate the binomial distribution.

Step-by-step explanation:

When the probability p of success in a Bernoulli trial is small, the Poisson distribution is often preferred to approximate the binomial distribution. This is because the Poisson distribution is a good approximation when the number of trials is large (usually greater than or equal to 20) and the probability of success is small (usually less than or equal to 0.05).

For example, if you have a large number of trials (n) and a small probability of success (p), such as 1000 trials with a probability of success 0.01, the Poisson distribution can be used instead of the binomial distribution.

In summary, when p is small, the Poisson distribution is usually preferred as an approximation of the binomial distribution.