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Let X1,.., X, be a random sample of size n from a distribution with pdf S0(1 + x)-(1+8) 0

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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Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

Let X, ..., X. be a random sample of size n from a distribution with pdf
f0(1 + x)-(1+)
0<x
f(x; 8) -
%3D
x<0
(a) Find the MLE O of 0.
(b) Find a complete sufficient statistic for 0.
(c) Find the CRLB for 1/0.
(d) Find the UMVUE of 1/0.
(e) Find the asymptotic normal distribution for 8 and also for 1(0) = 1/0.
(f) Find the UMVUE of 0.

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