a) Let X₁, X₂,..., X₁ denote a random sample from N(0, ²) distribution withprobability density function:1f(x; σ²) = ze 20 -∞0 < x < 00o√2πAnd let S² =be the estimator of a².i) Show whether or not that S² is an unbiased estimator of o²?ii) Show that S² is a consistent estimator of ².71

X~N(0, standard deviations σ 2)

Answered: a) Let X₁, X2X₁ denote a random sample…

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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Let X equal the IQ of a randomly selected American. Assume X ~ N( μ μ {"version":"1.1","math":"μ"} =100, σ σ {"version":"1.1","math":"σ"} =4). What is the probability that a randomly selected American has an IQ below 90?
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Let X1,., Xn all be independent exponential distributions all with the same parameter 2. What is the distribution of the minimum of (X1,. a) what is the distribution of the smallest order statistic Y, ? b) Specify both the pdf of the distribution and describe the distribution and its parameters. ,Xn)? In other words:
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a) Let X₁, X2X₁ denote a random sample from N(0, 2) distribution with probability density function: f(x;0²) = ze 20² 884x10 σ√₂π And let S² = be the estimator of o². 71 i) Show whether or not that S² is an unbiased estimator of a²? ii) Show that S² is a consistent estimator of a².