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Let = min{Snor Sna}, where is a positive integer, is a negative integer, and SX1 + X2 + ··· + Xn. Assume that {Xii≥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 a stopping rule? Why or why not? Hint: The more difficult part of this is to argue that 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 S?

(c) Find an expression for E [S] in terms of pa, and b, where = Pr{SJ ≥ a}.

(d) Find an expression for E [S] from Wald's equality. Use this to solve for p.

Text Book: Stochastic Processes: Theory for Applications By Robert G. Gallager.

Advanced Statistics, Statistics

  • Category:- Advanced Statistics
  • Reference No.:- M91582361

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