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Divide the total number of incidents by the total time. The result, representing the average number of incidents per unit of time, is the mean as well as the variance of the Poisson distribution.

Q: How do you calculate the mean and variance of a poisson distribution as a function of time t?

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The exponential distribution and the Poisson distribution.

The mean and variance are equal in the Poisson distribution. The mean and std deviation would be equal only for the case of mean = 1. See related link.

No. The variance of any distribution is the sum of the squares of the deviation from the mean. Since the square of the deviation is essentially the square of the absolute value of the deviation, that means the variance is always positive, be the distribution normal, poisson, or other.

Yes.

Why belong exponential family for poisson distribution

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The exponential distribution and the Poisson distribution.

yes

It is a discrete distribution in which the men and variance have the same value.

The mean and variance are equal in the Poisson distribution. The mean and std deviation would be equal only for the case of mean = 1. See related link.

No. The variance of any distribution is the sum of the squares of the deviation from the mean. Since the square of the deviation is essentially the square of the absolute value of the deviation, that means the variance is always positive, be the distribution normal, poisson, or other.

The Poisson distribution. The Poisson distribution. The Poisson distribution. The Poisson distribution.

The Poisson distribution is discrete.

Yes.

Why belong exponential family for poisson distribution

we compute it by using their differences

Using the Taylor series expansion of the exponential function. See related links

The MGF is exp[lambda*(e^t - 1)].