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Poisson Distribution. A Poisson random variable is the number of successes that result from a Poisson experiment. The probability distribution of a Poisson random variable is called a Poisson distribution. Given the mean number of successes (Î¼) that occur in a specified region, we can compute the Poisson probability based on the following formula:
Random variable \( X \) has the standard Cauchy distribution if \( X \) has a continuous distribution on \( \R \) with probability density function \( g \) given by \[ g(x) = \frac{1}{\pi \left(1 + x^2\right)}, \quad x \in \R \] Yes, \( g \) really is a probability density function.