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What does it mean for two random variables to be "identically distributed"? Does it mean that they come from the same probability distribution?

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Suppose $X$ and $Y$ are iid random variables. The 'identically distributed' part means both random variables have the same distribution function (cdf). Formally this can be stated as $$F_X(z)=F_Y(z),$$ where $F_X(\cdot)$ and $F_Y(\cdot)$ are the marginal cdfs of $X$ and $Y$, respectively. The 'independently distributed' part means the joint cdf of $X$ and $Y$, denoted $F_{XY}(x,y)$ is simply the product of the marginal cdfs $F_X(x)$ and $F_Y(y)$, i.e. $$F_{XY}(x,y)=F_X(x)F_Y(y).$$

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