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.
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ReneOnly 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.
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Can 2asquared be a binomial?
2 a2 is a monomial, not a binomial but 2 + a2 is a binomial, so is 2 - a2 .
What is the binomial factor of 2x-5?
(2x - 5) is a binomial factor
Is 8x binomial?
No, it is a monomial.
Is 6xy a binomial?
no or false
Is 5x2y plus 4x - 6 a binomial?
if the 5x2y means 5x2y + 4x - 6 then yes it is a binomial but if the 5x2y means 5x * 2y + 4x - 6 then no it is not a binomial a nomial means one degree. a binomial means something to the second power. a polynomial means anything that has a 3rd power and greater.
