Past exam of the mathematics course of the University of Cambridge / 2006 / iii / Paper 36 / 3 / b / ii

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- Solution ii

Solution

When

μ = E X > 0

, the event

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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