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Or, we can start with a function that satisfies the properties of a CDFfor eachxand then obtain a PDF – in the usual ways for discrete,continuous, or mixed random variables.8
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∙One sometimes starts with a joint distribution, finds the marginal ofX, and then obtainsfY|Xy|xusing the formula. But in the socialsciences it is much more common to directly specifyfY|Xy|xso thatfY|X.|xis a PDF for allx, often being silent on the distribution ofX.The idea is we are interested in howfY|X.|xchanges withx– forexample, how does the earnings distribution change with differentlevels of education?9