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: (i) 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 E(X200|X100 = 70]? Round your answer to the nearest integer.
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: (i) 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 E(X200|X100 = 70]? Round your answer to the nearest integer.
A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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![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:
(i) 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 Xp 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 E[X200|X100 = 70]? Round your answer to the nearest
integer.
Hint: consider Yn = Xn/(n + 2).
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F815f2e5b-f4d0-4ba3-88d9-27b4d72d9abe%2F11759d89-6739-4e84-8ac3-958635c73dc9%2Fw8tfqm_processed.png&w=3840&q=75)
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:
(i) 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 Xp 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 E[X200|X100 = 70]? Round your answer to the nearest
integer.
Hint: consider Yn = Xn/(n + 2).
%3D
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