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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 › Probability

“The maximum of independent exponentials is exponential” — false

Counterexample: max(X₁, X₂) with Xᵢ ~ Exp(1)

The minimum is exponential (rate $λ_{1} + λ_{2})$ ; the maximum has CDF (1 − $e^{- x})^{2}$ , which is not exponential.

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