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The human IQ is normally distributed with a mean of 100 points and a standard deviation of 15 points. A test measures the IQ with a standard deviation of 5 points. If someone scores 100 (or 150, 200) points on this test, what is a reasonable Bayesian estimate of his/her real IQ? Specifically, consider Xi~N(0,52) with a prior distribution on ; being ₂ ~ N(100, 15²). (a) Find the posterior distribution of 0; given Xi. 200, respectively? Do (b) What's the posterior expectation, E(0¿|X₁), for X₁ = 100, X2 = 150 and X3 = Bayesians appear to trust seemingly smart people or not? [Think: What's the statistical intuition behind their apparent trust or distrust?

The human IQ is normally distributed with a mean of 100 points and a standard deviation of 15 points. A test measures the IQ with a standard deviation of 5 points. If someone scores 100 (or 150, 200) points on this test, what is a reasonable Bayesian estimate of his/her real IQ? Specifically, consider Xi~N(0,52) with a prior distribution on ; being ₂ ~ N(100, 15²). (a) Find the posterior distribution of 0; given Xi. 200, respectively? Do (b) What's the posterior expectation, E(0¿|X₁), for X₁ = 100, X2 = 150 and X3 = Bayesians appear to trust seemingly smart people or not? [Think: What's the statistical intuition behind their apparent trust or distrust?

MATLAB: An Introduction with Applications
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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find the posterior distribution please

The human IQ is normally distributed with a mean of 100 points and a standard deviation of 15 points. A test measures the IQ with a standard deviation of 5 points. If someone scores 100 (or 150, 200) points on this test, what is a reasonable Bayesian estimate of his/her real IQ? Specifically, consider Xi ~ N(0i, 5²) with a prior distribution on ¤¿ being ; ~ N(100, 15²). (a) Find the posterior distribution of 0; given X₁. (b) What's the posterior expectation, E(0¿|Xi), for X1 = - 100, X2 150 and X3 = 200, respectively? Do Bayesians appear to trust seemingly smart people or not? [Think: What's the statistical intuition behind their apparent trust or distrust?]
Transcribed Image Text:The human IQ is normally distributed with a mean of 100 points and a standard deviation of 15 points. A test measures the IQ with a standard deviation of 5 points. If someone scores 100 (or 150, 200) points on this test, what is a reasonable Bayesian estimate of his/her real IQ? Specifically, consider Xi ~ N(0i, 5²) with a prior distribution on ¤¿ being ; ~ N(100, 15²). (a) Find the posterior distribution of 0; given X₁. (b) What's the posterior expectation, E(0¿|Xi), for X1 = - 100, X2 150 and X3 = 200, respectively? Do Bayesians appear to trust seemingly smart people or not? [Think: What's the statistical intuition behind their apparent trust or distrust?]
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