# Thread:

1. ## Another problem related to random walk...

Let ${X_n}$ be a symmetric simple random walk.

What is $P(X_7+X_{12} = X_1 + X_{16}$?

I tried to start this problem by setting a new variable $X_{7+X_{12}}$ and transfer the problem into the probability that two X equal but that lead no where. Is there any property that deal with the sum of random walk random variables? It would be great if someone could help me.
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