Let X (X1, X2,.,X) be a sample of i.i.d. Geometric() random variables with density function f(x;0) 0(1-0), z=0,1,2,...; 0Є (0,1), with mean and variance given by E(X)-1-0 and Var(X)-1--0 Note: This setup applies to all parts of this question. (a)-(c). a) A density f(r,) belongs to the one parameter exponential family density if 0 € 0 = R¹ and f(x,0) a(0)b(z) exp(c(0)d(z)) with c(0) strictly monotone. The Geometric(0) distribution belongs to the one-parameter exponential family and therefore we can find a complete and (minimal) sufficient statistic for 0. Find the functions that describe the Geometric distribution belonging to the one parameter exponential family density. a(0) = 0, b(x)=1, c(0)= log(1-0) and d(2)=logr - a(0) = log(1-0), b(x)=1, c(0)-10 and d(2)-log z a(0) log(1-0), b(x)=2, c(0) and d(2)=2 a(0) 0, b(z) 1, c(0)-log(0) and d(2)=2 a(0) 0, b(z) 1, c(0) - log(1-0) and d(2)-2

Let X (X1, X2,.,X) be a sample of i.i.d. Geometric() random variables with density function f(x;0) 0(1-0), z=0,1,2,...; 0Є (0,1), with mean and variance given by E(X)-1-0 and Var(X)-1--0 Note: This setup applies to all parts of this question. (a)-(c). a) A density f(r,) belongs to the one parameter exponential family density if 0 € 0 = R¹ and f(x,0) a(0)b(z) exp(c(0)d(z)) with c(0) strictly monotone. The Geometric(0) distribution belongs to the one-parameter exponential family and therefore we can find a complete and (minimal) sufficient statistic for 0. Find the functions that describe the Geometric distribution belonging to the one parameter exponential family density. a(0) = 0, b(x)=1, c(0)= log(1-0) and d(2)=logr - a(0) = log(1-0), b(x)=1, c(0)-10 and d(2)-log z a(0) log(1-0), b(x)=2, c(0) and d(2)=2 a(0) 0, b(z) 1, c(0)-log(0) and d(2)=2 a(0) 0, b(z) 1, c(0) - log(1-0) and d(2)-2

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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