Relations between the Distributions

Relation between Bernoulli and Binomial Distribution

1. Bernoulli Distribution is a special case of Binomial Distribution with a single trial.

2. There are only two possible outcomes of a Bernoulli and Binomial distribution, namely success and failure.

3. Both Bernoulli and Binomial Distributions have independent trails.

Relation between Poisson and Binomial Distribution

Poisson Distribution is a limiting case of binomial distribution under the following conditions:

1. The number of trials is indefinitely large or n → ∞.
2. The probability of success for each trial is same and indefinitely small or p →0.
3. np = λ, is finite.

Relation between Normal and Binomial Distribution & Normal and Poisson Distribution:

Normal distribution is another limiting form of binomial distribution under the following conditions:

1. The number of trials is indefinitely large, n → ∞.
2. Both p and q are not indefinitely small.

The normal distribution is also a limiting case of Poisson distribution with the parameter λ →∞.

Relation between Exponential and Poisson Distribution:

If the times between random events follow exponential distribution with rate λ, then the total number of events in a time period of length t follows the Poisson distribution with parameter λt.