Aggregation reduces the standard deviation of demand only if demand across the regions being aggregated is perfectly

Question:

Aggregation reduces the standard deviation of demand
only if demand across the regions being aggregated is perfectly positively correlated.

only if demand across the regions being aggregated is not perfectly positively correlated.
even if demand across the regions being aggregated is not perfectly positively correlated.
whenever demand across the regions being aggregated is not perfectly uncorrelated.

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