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$X$ and $Y$ are iid Bernoulli($p$), then what's the marginal pmf and joint pmf for $\max(X, Y)$ and $\min(X, Y)$?

Not sure if I can use the formula for marginal order statistics pmf here.

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    Hint: $(X,Y)$ can have four different values. Make a table with four rows and five columns. On each row, write the values of $X$, $Y$,the probability that $(X,Y)$ has these values (sub-hint: iid Bernoulli$(p)$ might help), $\max(X,Y)$, and $\min(X,Y)$. Stare very hard at the array that you have created.2012-08-03
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    I do not know what you call *the formula for marginal order statistics pmf* but you could simply enumerate the values of $(i,j)$ such that the event $[\max(X,Y)=i,\min(X,Y)=j]$ is not empty and compute its probability.2012-08-03

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