answersLogoWhite

0

Only in certain circumstances:

The probability of success, p, in each trial must be close to 0.

Then, for the random variable, X = number of successes in n trials, the mean is np

and the variance is np(1-p). But since p is close to 0, (1-p) is close to 1 and so np(1-p) is close to np.

That is, the mean of the distribution is close to its variance. This is a characteristic of the Poisson distribution.

Furthermore, the other characteristics of the distribution: constant probability, independence are met so the Binomial can be approximated by the Poisson.

It is possible to prove this analytically but the limitations of this browser - especially in terms of mathematical notation - preclude that.

Only in certain circumstances:

The probability of success, p, in each trial must be close to 0.

Then, for the random variable, X = number of successes in n trials, the mean is np

and the variance is np(1-p). But since p is close to 0, (1-p) is close to 1 and so np(1-p) is close to np.

That is, the mean of the distribution is close to its variance. This is a characteristic of the Poisson distribution.

Furthermore, the other characteristics of the distribution: constant probability, independence are met so the Binomial can be approximated by the Poisson.

It is possible to prove this analytically but the limitations of this browser - especially in terms of mathematical notation - preclude that.

Only in certain circumstances:

The probability of success, p, in each trial must be close to 0.

Then, for the random variable, X = number of successes in n trials, the mean is np

and the variance is np(1-p). But since p is close to 0, (1-p) is close to 1 and so np(1-p) is close to np.

That is, the mean of the distribution is close to its variance. This is a characteristic of the Poisson distribution.

Furthermore, the other characteristics of the distribution: constant probability, independence are met so the Binomial can be approximated by the Poisson.

It is possible to prove this analytically but the limitations of this browser - especially in terms of mathematical notation - preclude that.

Only in certain circumstances:

The probability of success, p, in each trial must be close to 0.

Then, for the random variable, X = number of successes in n trials, the mean is np

and the variance is np(1-p). But since p is close to 0, (1-p) is close to 1 and so np(1-p) is close to np.

That is, the mean of the distribution is close to its variance. This is a characteristic of the Poisson distribution.

Furthermore, the other characteristics of the distribution: constant probability, independence are met so the Binomial can be approximated by the Poisson.

It is possible to prove this analytically but the limitations of this browser - especially in terms of mathematical notation - preclude that.

User Avatar

Wiki User

11y ago

Still curious? Ask our experts.

Chat with our AI personalities

JordanJordan
Looking for a career mentor? I've seen my fair share of shake-ups.
Chat with Jordan
BeauBeau
You're doing better than you think!
Chat with Beau
TaigaTaiga
Every great hero faces trials, and you—yes, YOU—are no exception!
Chat with Taiga
More answers

Only in certain circumstances:

The probability of success, p, in each trial must be close to 0.

Then, for the random variable, X = number of successes in n trials, the mean is np

and the variance is np(1-p). But since p is close to 0, (1-p) is close to 1 and so np(1-p) is close to np.

That is, the mean of the distribution is close to its variance. This is a characteristic of the Poisson distribution.

Furthermore, the other characteristics of the distribution: constant probability, independence are met so the Binomial can be approximated by the Poisson.

It is possible to prove this analytically but the limitations of this browser - especially in terms of mathematical notation - preclude that.

User Avatar

Wiki User

11y ago
User Avatar

Add your answer:

Earn +20 pts
Q: Why binomial distribution can be approximated by Poisson distribution?
Write your answer...
Submit
Still have questions?
magnify glass
imp