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#reading-10-common-probability-distributions

For example, a discrete random variable *X* can take on a limited number of outcomes *x*_{1}, *x*_{2}, …, *x*_{n} (*n* possible outcomes), or a discrete random variable *Y* can take on an unlimited number of outcomes *y*_{1}, *y*_{2}, … (without end).1 Because we can count all the possible outcomes of *X* and *Y* (even if we go on forever in the case of *Y*), both *X* and *Y* satisfy the definition of a discrete random variable. By contrast, we cannot count the outcomes of a continuous random variable. We cannot describe the possible outcomes of a continuous random variable *Z* with a list *z*_{1}, *z*_{2}, … because the outcome (*z*_{1} + *z*_{2})/2, not in the list, would always be possible. Rate of return is an example of a continuous random variable.

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