what is the parameter of the poisson distribution
Poisson distribution In probability theory and statistics, the Poisson distribution (French pronunciation [pwaˈsɔ̃]; in English often rendered /ˈpwɑːsɒn/), named after French mathematician Siméon Denis Poisson, is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant rate and independently of the time since the last event.[1] The Poisson distribution can also be used for the number of events in other specified intervals such as distance, area or volume.
Mean The mean of a probability distribution is the long-run arithmetic average value of a random variable having that distribution. In this context, it is also known as the expected value. For a discrete probability distribution, the mean is given by   ∑ x P ( x )  {\displaystyle \textstyle \sum xP(x)} , where the sum is taken over all possible values of the random variable and   P ( x )  {\displaystyle P(x)}  is the probability mass function. For a continuous distribution,the mean is    ∫ − ∞  ∞  x f ( x ) d x  {\displaystyle \textstyle \int _{-\infty }^{\infty }xf(x)\,dx} , where   f ( x )  {\displaystyle f(x)}  is the probability density function. In all cases, including those in which the distribution is neither discrete nor continuous, the mean is the Lebesgue integral of the random variable with respect to its probability measure. The mean need not exist or be finite; for some probability distributions the mean is infinite (+∞ or −∞), while others have no mean.
1 + 2 + 3 + 4 + ⋯ which increases without bound as n goes to infinity. Because the sequence of partial sums fails to converge to a finite limit, the series does not have a sum.
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