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I have this probability:

[tex]\text{Pr}\left\{\underset{i,j}{\max\,}\underset{n}{\min\,}X_i(n)+X_j(n)<a\right\}[/tex]

where X_i(n) and X_j(n) are i.i.d. for all i,j, and n. Can I find the distribution of

[tex]X_i(n_{\text{min}})[/tex]

where:

[tex]\underset{n}{\min\,}X_i(n)+X_j(n)=X_i(n_{\text{min}})+X_j(n_{\text{min}})[/tex]

??

Thanks in advance

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# Max min distribution problem

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