In his 1789 article, Bayes described a scenerio in which 6 balls are distributed independently and uniformly on a billiards table. A white ball defines a line, and you are told the count X of how many of n = 5 red balls end up to the left of that line. If we define the table to have length 1, we may assume the positions (left-to-right) of the balls are all distributed iid Uniform(0,1), with marking the position of the white ball and X counting the number of balls whose uniform variable ends up being less than 0. a) Given 0, what is the distribution of X, the count of uniform values less than 0? b) Find the marginal pmf for X, unconditional on 0. c) You are told X = 0. Find the conditional (posterior) distribution for given X = 0. Sketch the pdf for this distribtion.
In his 1789 article, Bayes described a scenerio in which 6 balls are distributed independently and uniformly on a billiards table. A white ball defines a line, and you are told the count X of how many of n = 5 red balls end up to the left of that line. If we define the table to have length 1, we may assume the positions (left-to-right) of the balls are all distributed iid Uniform(0,1), with marking the position of the white ball and X counting the number of balls whose uniform variable ends up being less than 0. a) Given 0, what is the distribution of X, the count of uniform values less than 0? b) Find the marginal pmf for X, unconditional on 0. c) You are told X = 0. Find the conditional (posterior) distribution for given X = 0. Sketch the pdf for this distribtion.
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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Transcribed Image Text:In his 1789 article, Bayes described a scenerio in which 6 balls are distributed independently and
uniformly on a billiards table. A white ball defines a line, and you are told the count X of how many
of n = 5 red balls end up to the left of that line. If we define the table to have length 1, we may
assume the positions (left-to-right) of the balls are all distributed iid Uniform(0,1), with 0 marking
the position of the white ball and X counting the number of balls whose uniform variable ends up
being less than 0.
a) Given 0, what is the distribution of X, the count of uniform values less than 0?
b) Find the marginal pmf for X, unconditional on 0.
c) You are told X = 0. Find the conditional (posterior) distribution for 0 given X = 0. Sketch the
pdf for this distribtion.
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