MIT6_262S11_lec20

# Consider a sample space containing a rv h the hy

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Unformatted text preview: + wn = yn−1 + wn−1 If arrival n sees an empty queue, then wn = 0. 16 wn = yn−1 − xn + wn−1 if wn−1 + yn−1 ≥ xn else wn = 0 wn = max[wn−1 + yn−1 − xn, 0] Since this is true for all sample paths, Wn = max[Wn−1 + Yn−1 − Xn, 0] Deﬁne Un = Yn−1 − Xn. Then Wn = max[Wn−1 + Un, 0] Without the max, {Wn; n ≥ 1} would b e a random walk based on {Ui; i ≥ 1}. With the max, {Wn; n ≥ 1} is like a random walk, but it resets to 0 every time it goes negative. The text restates this in an alternative manner. 17 Detection, decisions, & Hypothesis testing These are diﬀerent names for the same thing. Given observations, a decision must b e made b etween a set of alternatives. Here we consider only binary decisions, i.e., a choice between two hypotheses. Consider a sample space containing a rv H (the hy­ pothesis) with 2 p ossible values, H = 0 and H = 1. The PMF for H , pH (0) = p0, pH (1) = p1, is called the a priori probabilities of H . Assume n observations, Y1, . . . , Yn are made. These are IID conditional on H = 0 and I ID conditional on H =...
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## This note was uploaded on 01/13/2012 for the course ELECTRICAL 6.262 taught by Professor Staff during the Fall '11 term at MIT.

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