Let Y Poisson(A), with A > 0. Then, show that Tchebysheff's inequality gives P (0 1

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Q: 4. Determine whether the function g(x) = roo sin²x converges or diverges by comparing it to f(x)…

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Q: ssume X ∼ Poisson(r), where r > 0. Prove that E(X) = r.

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Q: Q2/Find the limiting values: lim Tan (4%) 必→。 O lim 7 7- x2

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Q: Use series to evaluate the limit. 1- cos(5x) lim x → 0 1 + 5x – e5x

A: Authoring guidelines: As per the authoring guidelines we can solve only the first question.Please…