Consider an urn which contains red balls and green balls. Initially there is just one green ball and one red ball in the urn. At each time step a ball is chosen randomly from the urn: (1) If the ball is red, then it's returned to the urn with an additional red ball; (i) if the ball is green, then it's returned to the urn with an additional green ball. Let Xn denote the number of red balls in the urn after n draws. Suppose after 100 draws, there are 70 red balls, that is X100 = 70. What is the expected number of red balls in the urn after another 100 draws, that is B(X200|X100 = 70|? Round your answer to the nearest integer. Hint: consider Yn = Xn/(n + 2).
Consider an urn which contains red balls and green balls. Initially there is just one green ball and one red ball in the urn. At each time step a ball is chosen randomly from the urn: (1) If the ball is red, then it's returned to the urn with an additional red ball; (i) if the ball is green, then it's returned to the urn with an additional green ball. Let Xn denote the number of red balls in the urn after n draws. Suppose after 100 draws, there are 70 red balls, that is X100 = 70. What is the expected number of red balls in the urn after another 100 draws, that is B(X200|X100 = 70|? Round your answer to the nearest integer. Hint: consider Yn = Xn/(n + 2).
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:6. Consider an urn which contains red balls and green balls. Initially there is just one green
ball and one red ball in the urn. At each time step a ball is chosen randomly from the urn:
() If the ball is red, then it's returned to the urn with an additional red ball; (ii) if the ball is
green, then it's returned to the urn with an additional green ball.
Let Xn denote the number of red balls in the urn after n draws. Suppose after 100 draws,
there are 70 red balls, that is X100 = 70. What is the expected number of red balls in the
urn after another 100 draws, that is B[x200|X100 = 70|? Round your answer to the nearest
integer.
Hint: consider Yn = Xn/(n+2).
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