Gayatri can only walk on a straight line. She starts at a given point and every second she moves either forward
or backwards with equal probability. Let n be the expected number of steps before she returns to her starting
point? Answer the integer part of 4900/n.
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- The random walk is simple if Xk = ±1, with P(Xk = 1) = p and P(Xk = −1) = 1−p = q. Imagine a particle performing a random walk on the integer points of the real line, where it in each step moves to one of its neighboring points; see Figure 1. Remark 1. You can also study random walks in higher dimensions.
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