Relationships between Distribution

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 \({n\to\infty}\)

  2. The probability of success for each trial is same and indefinitely small or \({p\to 0}\)

  3. np = \({\lambda}\), 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, \({n\to\infty}\)
  2. Both p and q are not indefinitely small.
  3. The normal distribution is also a limiting case of Poisson distribution with the parameter \({\lambda\to\infty}\).

Relation between Exponential and Poisson Distribution:

If the times between random events follow exponential distribution with rate \({\lambda}\), then the total number of events in a time period of length t follows the Poisson distribution with parameter \({\lambda}\)t.