Q6 At all times, an urn contains N balls- some white balls and some black balls. At each stage, a coin having probability p, 0
Q6 At all times, an urn contains N balls- some white balls and some black balls. At each stage, a coin having probability p, 0
MATLAB: An Introduction with Applications
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Chapter1: Starting With Matlab
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
Transcribed Image Text:Q6 At all times, an urn contains N balls- some white balls and some black balls. At each stage, a
coin having probability p, 0 < p < 1, of landing heads, is flipped. If heads appear, then a ball is
chosen at random from the urn and is replaced by a white ball; if tails appear, then a ball is chosen
from the urn and is replaced by a black ball. Let Xn denote the number of white balls in the urn
after the n stages.
Q6(i.) Is {Xn, n 2 0} a Markov Chain? If so, explain why.
Q6(ii.) Compute the transition probabilities Pij: (Hint: At some stage, suppose there are i white
balls (and N – i black balls). Think how you can get i or i – 1 or i +1 white balls in the next
stage.)
Q6(iii.) Let N
2. Then the states are 0, 1, 2 and the transition probability matrix is given by
를 + 올 끌
Find the proportion of the time in each state.
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