 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2006/iii/paper-36/3/b/ii/solution

Codex  0 Created 2026-10-03 Updated 2026-10-14

When

μ = E X > 0

X = 0

implies

∣ X - μ ∣ \geq μ

. The Chebyshev inequality therefore gives

P (X = 0) \leq \frac{Var ( X )}{( E X ) ^{2}} .

This is the second moment method for proving that a nonnegative count is positive.

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