Q3 Suppose we have two boxes and 2N cards, of which N are blue and N are red. Initially, N of the cards are placed in box 1, and the remainder of the cards are placed in box 2. At each trial a card is chosen at random from each of the boxes, and the two cards are put back in the opposite boxes. Let Xo denote the number of blue cards initially in box 1 and, let Xn for n ≥ 1, be the number of blue cards in box 1 after the nth trial. Find the closed form transition probailities of the Markov chain Xn, n ≥ 0.

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Q3 Suppose we have two boxes and 2N cards, of which N are blue and N are red. Initially,
N of the cards are placed in box 1, and the remainder of the cards are placed in box
2. At each trial a card is chosen at random from each of the boxes, and the two cards
are put back in the opposite boxes. Let Xo denote the number of blue cards initially
in box 1 and, let Xn for n ≥ 1, be the number of blue cards in box 1 after the nth
trial. Find the closed form transition probailities of the Markov chain Xn, n ≥ 0.
Transcribed Image Text:Q3 Suppose we have two boxes and 2N cards, of which N are blue and N are red. Initially, N of the cards are placed in box 1, and the remainder of the cards are placed in box 2. At each trial a card is chosen at random from each of the boxes, and the two cards are put back in the opposite boxes. Let Xo denote the number of blue cards initially in box 1 and, let Xn for n ≥ 1, be the number of blue cards in box 1 after the nth trial. Find the closed form transition probailities of the Markov chain Xn, n ≥ 0.
Expert Solution
Step 1

Given that

         we have 2 boxes and 2N cards, of which N are blue and N are red

Here we want to find

                P(x,y)=PXn+1=y Xn=x

steps

Step by step

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