Define a sequence X 1 , , X n of independent random variables such that for each k 1, , n, X k 1, with probability 1 2 each Let S X 1 X n This model describes a simple symmetric random walk that starts at the origin and moves left or right at each unit of time Find E S and V S

Question: Define a sequence X 1 , . . . , X n of independent random variables such that for each k = 1, . .

Define a sequence X₁, . . . , X_n of independent random variables such that for each k = 1, . . . , n, X_k = ±1, with probability 1/2 each. Let S = X₁ +· · · + X_n. This model describes a simple symmetric random walk that starts at the origin and moves left or right at each unit of time. Find E[S] and V[S].

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