Paper 2, Section I, F

Probability | Part IA, 2018

(a) State the Cauchy-Schwarz inequality and Markov's inequality. State and prove Jensen's inequality.

(b) For a discrete random variable XX, show that Var(X)=0\operatorname{Var}(X)=0 implies that XX is constant, i.e. there is xRx \in \mathbb{R} such that P(X=x)=1\mathbb{P}(X=x)=1.

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