Prove, starting from the definition of convergence in probability : (a) Op (1) + 0p (1) = Op (1) (b) Op (1) Op (1) = 0p (1) (c) g(μ+op (1)) = g(µ) +op (1), g (.) is continuous at μ.

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Prove, starting from the definition of convergence in probability :
(a) op (1) + Op (1) = op (1)
(b) op (1) Op (1) = 0p (1)
(c) g(u+ op (1)) = g (µ) + Op (1), g(·) is continuous at u.
Transcribed Image Text:Prove, starting from the definition of convergence in probability : (a) op (1) + Op (1) = op (1) (b) op (1) Op (1) = 0p (1) (c) g(u+ op (1)) = g (µ) + Op (1), g(·) is continuous at u.
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