Is the following statement true? The maximum of independent exponentials is exponential

No. max(X₁, X₂) with Xᵢ ~ Exp(1) The *minimum* is exponential (rate λ₁+λ₂); the maximum has CDF (1 − e^{−x})², which is not exponential.

Counterexample

Is this true?

The maximum of independent exponentials is exponential

No — it is false.

The counterexample

$\max(X_{1}, X_{2})$ with $X_{i}$ ~ Exp(1)

Why it fails

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

Keep practicing

Invariants don't determine

Two objects sharing an invariant were treated as the same object.

Published 23 Aug 2026. Found a mistake? Tell us — corrections are the fastest thing we act on.