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Which distribution function has equal mean and variance?
The exponential distribution and the Poisson distribution.
Moment generating and the cumulant generating function of poisson distribution?
The moment generating function is M(t) = Expected value of e^(xt) = SUM[e^(xt)f(x)] and for the Poisson distribution with mean a inf = SUM[e^(xt).a^x.e^(-a)/x!] x=0 inf = e^(-a).SUM[(ae^t)^x/x!] x=0 = e^(-a).e^(ae^t) = e^[a(e^t -1)]
If X has Poisson distribution does aX plus b have Poisson Distribution?
Yes.
Why belong exponential family for poisson distribution or geometric distribution?
Why belong exponential family for 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.
How do you obtain the moment generating function of a Poisson distribution?
Using the Taylor series expansion of the exponential function. See related links
Which distribution function has equal mean and variance?
The exponential distribution and the Poisson distribution.
Moment generating and the cumulant generating function of poisson distribution?
The moment generating function is M(t) = Expected value of e^(xt) = SUM[e^(xt)f(x)] and for the Poisson distribution with mean a inf = SUM[e^(xt).a^x.e^(-a)/x!] x=0 inf = e^(-a).SUM[(ae^t)^x/x!] x=0 = e^(-a).e^(ae^t) = e^[a(e^t -1)]
Which distribution is used to find probabilities about the number of independent events occurring in a fixed time period with a known average rate?
The Poisson distribution. The Poisson distribution. The Poisson distribution. The Poisson distribution.
Is the Poisson probability distribution discrete or continuous?
The Poisson distribution is discrete.
If X has Poisson distribution does aX plus b have Poisson Distribution?
Yes.
Why belong exponential family for poisson distribution or geometric distribution?
Why belong exponential family for poisson distribution
How do you compute the probability distribution of a function of two Poisson random variables?
we compute it by using their differences
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.
What is the difference between poisson distribution and poisson process?
A poisson process is a non-deterministic process where events occur continuously and independently of each other. An example of a poisson process is the radioactive decay of radionuclides. A poisson distribution is a discrete probability distribution that represents the probability of events (having a poisson process) occurring in a certain period of time.
What is the difference between poisson and binomial distribution?
Poisson and Binomial both the distribution are used for defining discrete events.You can tell that Poisson distribution is a subset of Binomial distribution. Binomial is the most preliminary distribution to encounter probability and statistical problems. On the other hand when any event occurs with a fixed time interval and having a fixed average rate then it is Poisson distribution.
Poisson distribution the mean and standard deviation?
The Poisson distribution is a discrete distribution, with random variable k, related to the number events. The discrete probability function (probability mass function) is given as: f(k; L) where L (lambda) is the mean and square root of lambda is the standard deviation, as given in the link below: http://en.wikipedia.org/wiki/Poisson_distribution
