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Counterexample bank

Part C is won by knowing which tempting claims are false. 148 counterexamples; 85 free. The rest come with the Notes pack.

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#1 · Probability & Statistics › Linear Models and Multivariate

“If every marginal is normal then the vector is multivariate normal” — false

Counterexample: X ~ N(0,1) and Y = εX with ε = ±1 independent

Both marginals are N(0,1) but X + Y is 0 half the time — not normal, so the pair is not jointly normal.

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