Two players, \(P_1\) and \(P_2\), play a game against each other. In every round of the game, ea....

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Two players, \(P_1\) and \(P_2\), play a game against each other. In every round of the game, each player rolls a fair die once, where the six faces of the die have six distinct numbers. Let x and y denote the readings on the die rolled by \(P_1\) and \(P_2\), respectively. If x>y, then \(P_1\) scores 5 points and \(P_2\) scores 0 point. If x=y, then each player scores 2 points. If x<y, then \(P_1\) scores 0 point and \(P_2\) scores 5 points. Let \(X_i\) and \(Y_i\) be the total scores of \(P_1\) and \(P_2\), respectively, after playing the \(i^{\text {th }}\) round
 
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