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 X₁N(0, 52) with a prior distribution on 0; being 0%; ~ N(100, 15²). (a) Find the posterior distribution of 0; given X₂. (b) What's the posterior expectation, E(X), 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?

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 X₁N(0, 52) with a prior distribution on 0; being 0%; ~ N(100, 15²). (a) Find the posterior distribution of 0; given X₂. (b) What's the posterior expectation, E(X), 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?

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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