Reference no: EM13909426
Let J = min{n | Sn≤b or Sn≥a}, where a is a positive integer, b is a negative integer, and Sn = X1 + X2 + ··· + Xn. Assume that {Xi; i≥1} is a set of zero- mean IID rv s that can take on only the set of values {-1, 0, +1}, each with positive probability.
(a) Is J a stopping rule? Why or why not? Hint: The more difficult part of this is to argue that J is a rv (i.e., non-defective); you do not need to construct a proof of this, but try to argue why it must be true.
(b) What are the possible values of SJ ?
(c) Find an expression for E [SJ ] in terms of p, a, and b, where p = Pr{SJ ≥ a}.
(d) Find an expression for E [SJ ] from Wald's equality. Use this to solve for p.
Text Book: Stochastic Processes: Theory for Applications By Robert G. Gallager.
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