Sums of Normally distributed stochastic variables (a) (X_{1} sim phi_{(0,1)}, X_{2} sim phi_{(-1,3)}, X_{3} sim phi_{(2,4)}, X_{4}

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Sums of Normally distributed stochastic variables

(a) $X_{1} \sim \phi_{(0,1)}, X_{2} \sim \phi_{(-1,3)}, X_{3} \sim \phi_{(2,4)}, X_{4} \sim \phi_{(2,2)}$. These four stochastic variables are independent, and $X=X_{1}+X_{2}+X_{3}+X_{4}$. What is the distribution of $X$ ?

(b) $X_{k} \sim \phi_{(2,4)}$, and $X=\sum_{k=1}^{10} X_{k}$. What is the distribution of $X$ ?

(c) $X_{k} \sim \phi_{(7,4)}, k=1,2,3,4$. Let $X$ be the average of the $X_{k}$. What is the distribution of $X$ ?

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The Bayesian Way Introductory Statistics For Economists And Engineers

ISBN: 9781119246879

1st Edition

Authors: Svein Olav Nyberg

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Question Posted: Mar 17, 2024 08:00 AM

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Sums of Normally distributed stochastic variables (a) (X_{1} sim phi_{(0,1)}, X_{2} sim phi_{(-1,3)}, X_{3} sim phi_{(2,4)}, X_{4}

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The Bayesian Way Introductory Statistics For Economists And Engineers

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