Here are ?? baseball teams, where ?? is an integer larger than 1. Each pair of the teams plays one game.
Suppose that, for every ?? = 1,2, ... , ??, the team ?? wins ???? games and loses ???? games. Then, choose all the wrong statements from (a) – (d) below.
(Here, the notation ∑?? ?? means ?? +?? + ⋯+ ?? )
??=1?? 12 ?? (a)??=??, where ??=∑?? ?? and ??=∑?? ??
(b)∑?? ??2 =∑?? ??2 ??=1 ?? ??=1 ??
??=1 ?? ??=1 ??
(c)∑?? (?? − ??)2 =∑?? (?? − ??)2 ??=1 ?? ??=1 ??
(d) All the above (a), (b) and (c) are wrong.
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Here are ?? baseball teams, where ?? is an integer larger than 1. Each pair of the teams plays one game. Suppose that, for every ?? = 1,2, ... , ??, the team ?? wins ???? games and loses ???? games. Then, choose all the wrong statements from (a) – (d) bel