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What is marginal distribution?

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Marginal distribution is a measurement used in the fields of statistics and probability theory to determine the probability of different values of variables in a subset of random variables without reference to any possible values of the other variables. Marginal distribution is the opposite of conditional distribution, in which the probability of a value of a variable is determined while referencing the possible values of the other variables.

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Marginal distribution is often used when attempting to calculate the overall probability of a variable, not the probability of that variable based off of other factors. For instance, suppose a statistician wants to determine the probability distribution that someone nearby speaks English. Of course, whether or not a nearby person speaks English is largely determined by several variables, such as what country the statistician is in.

If the statistician were to break down the probability that a nearby person speaks English in each country, the statistician would be using conditional distribution. Instead, the statistician would be using marginal distribution if he or she completely disregarded the country variable and simply wanted to know the possibility distribution overall of whether or not a nearby person speaks English in any random location. Marginal distribution is used not to determine the likelihood of certain outcomes, but instead to determine every possible outcome.

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