Show that, if G(z) is the g.f. of a r.v. X, then G(1) = E{X(X 1)}. How

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Show that, if G(z) is the g.f. of a r.v. X, then G″(1) = E{X(X −1)}. How to find Var{X} using the g.f. G(z)? Do that for the second version of the geometric distribution.

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Probability And Stochastic Modeling

ISBN: 9781439872062

1st Edition

Authors: Vladimir I. Rotar

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Question Posted: Jan 05, 2024 01:00 PM

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Show that, if G(z) is the g.f. of a r.v. X, then G(1) = E{X(X 1)}. How

Question:

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Since Gx z Ez we have G z E EXX1 and hence G1EXX1 Consequently VarX EXX...View the full answer

Probability And Stochastic Modeling

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