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Let X be a random variable having finite expectation

Let X be a random variable having finite expectation μ and variance σ2, and let g(∙) be a twice differentiable function. Show that

Expand g(∙) in a Taylor series about μ. Use the first three terms and ignore the remainder.

Expand g(∙) in a Taylor series about μ. Use the first three terms and ignore the remainder.

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