The union bound
WebCS174 Lecture 10 John Canny Chernoff Bounds Chernoff bounds are another kind of tail bound. Like Markoff and Chebyshev, they bound the total amount of probability of some random variable Y that is in the “tail”, i.e. far from the mean. Recall that Markov bounds apply to any non-negative random variableY and have the form: Pr[Y ≥ t] ≤Y Web2.6.1 The Union Bound The Robin to Chernoff-Hoeffding’s Batman is the union bound. It shows how to apply this single bound to many problems at once. It may appear crude, but can usually only be significantly improved if special structure is available in the class of problems. Theorem 2.6.4. Consider tpossibly dependent random events X 1 ...
The union bound
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WebFurthermore, a useful upper bound on the average symbol error probability is also obtained through the union bound. The analysis is applied to the sparse code multiple access (SCMA) systems.... WebWe note that the above proof can be extendend using the union bound and reproving a bound on ≤ −ε (setting Z′ i = 1−Zi) to give P Xm i=1 Xi − Xm i=1 E[Xi] ≥ mε! ≤ 2exp −2ε2m2 Pm i=1(bi −ai)2 . 3 McDiarmid’s Inequality This more general result, of which Hoeffding’s Inequality can be seen as a special case, is very useful in
Web1 hour ago · Leinster reveal Jacques Nienaber to join province as South Africa head coach to succeed Racing 92-bound Stuart Lancaster. Andrew Ryan; Published: 14:26, ... Most read … Web4. (Signal-space-based constellation design that minimizes the union bound) Suppose <= Sm+n, where 1 sm SM = 3, and 2, Sm and n are 2-dimensional vectors. Assume the prior probability for each sm is 1/3 and n is zero-mean Gaussian distributed with covariance matrix oʻI, where I is the 2 x 2 identity matrix. (a) (basic=4 pts., extra=2 pts.)
WebApr 15, 2024 · 39 W Union Ave , Bound Brook, NJ 08805-1715 is a single-family home listed for-sale at $448,000. The sq. ft. home is a 3 bed, 3.0 bath property. View more property details, sales history and Zestimate data on Zillow. MLS # 3838268 WebThe main advantage of the union bound is that it does not concern the dependency of bad events; however, there is a trade-o . The Union Bound is in fact a weak bound, meaning …
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