Take the Gamblers ruin on [0, N] with a fair coin, i.e., a simple random walk with absorbing boundaries at 0 and N. Let T be the time which elapses before the SRW is absorbed by one of the boundaries (i.e., the duration of the game. Show that P(T < ∞) = 1 and Epecation (T^k) < ∞ for all k.

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.