Any two independent r.v. X, Y are positively correlated with X+Y, obv. Given fixed X+Y=C, cov(X,Y | X+Y=C) = -1 cc: @themattsimpson
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Any two independent r.v. X, Y are positively correlated with X+Y, obv. Given fixed X+Y=C, cov(X,Y | X+Y=C) = -1 cc: @themattsimpson