Using the convolution formula, show that the sum of two independent standard normal r.v.s is normal with

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Using the convolution formula, show that the sum of two independent standard normal r.v.’s is normal with mean 0 and variance 2 (which is consistent with Proposition 5). (Advice: First, show that

Completing the square, write

and use the change of variables y−x/2 = s/√2.)

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Probability And Stochastic Modeling

ISBN: 9781439872062

1st Edition

Authors: Vladimir I. Rotar

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Question Posted: Jan 11, 2024 09:02 AM

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Using the convolution formula, show that the sum of two independent standard normal r.v.s is normal with

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Denoting by px the standard normal density and apply...View the full answer

Probability And Stochastic Modeling

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