Prove, starting from the definition of convergence in probability (a) $o p (1) o p (1) o p (1)$ (b) $o p (1) o p (1) 0 p (1)$ (c) $g left( mu o p (1) ight) g( mu) o p (1), g( cdot) $ is continuous at $ mu$ SP JG 006

Question

Prove, starting from the definition of convergence in probability   (a) $o  p (1) o  p (1) o  p (1)$ (b) $o  p (1) o  p  (1) 0  p  (1)$ (c) $g left( mu o  p  (1) ight) g( mu) o  p (1), g( cdot) $ is continuous at $ mu$  SP JG  006

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Question

Prove, starting from the definition of convergence in probability : (a) $o_{p}(1)+o_{p}(1)=o_{p}(1)$ (b) $o_{p}(1) o_{p} (1)=0_{p} (1)$ (c) $gleft(mu+o_{p} (1) ight)=g(mu)+o_{p}(1), g(cdot) $ is continuous

Prove, starting from the definition of convergence in probability : (a) $o_{p}(1)+o_{p}(1)=o_{p}(1)$ (b) $o_{p}(1) o_{p} (1)=0_{p} (1)$ (c) $g\left(\mu+o_{p} (1) ight)=g(\mu)+o_{p}(1), g(\cdot) $ is continuous at $\mu$. SP.JG. 006

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