Question: Let S _ ( n ) be a statistic with p lim _ ( ) S _ ( n ) = theta .

Let S_(n) be a statistic with p\lim_()S_(n)=\theta . Let g(*) be a differentiable function.
Prove from first principals that
p\lim_()g(S_(n))=g(\theta )
Let S _ ( n ) be a statistic with p \ lim _ ( ) S

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