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547概率简单数值题short

Hitting Time on K₄ Minus One Edge

题目

Take the complete graph K4K_4 on vertices {1,2,3,4}\{1,2,3,4\} and remove edge {1,4}\{1,4\}. The resulting graph has 55 edges, with d(1)=d(4)=2d(1)=d(4)=2 and d(2)=d(3)=3d(2)=d(3)=3. A simple random walk moves at each step to a uniformly random neighbor. Starting from vertex 22, what is the expected number of steps to reach vertex 44?

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