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Which distribution function has equal mean and variance?
The exponential distribution and the Poisson distribution.
How do you calculate the mean and variance of a poisson distribution as a function of time t?
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.
Are the mean and standard deviation equal in a 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.
Can the variance of a normally distributed random variable be negative?
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.
If X has Poisson distribution does aX plus b have Poisson Distribution?
Yes.
