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1 Sets x ∈ A means x is an element of A x 6∈A means x is not an element of A There are two notations for describing sets List A = {1,3,5,7,9} In December of 16, Winchester began offering special 30 WCF "Short Range" ammunition to be used for "small game where the more powerful cartridge is not necessary" as it was described in that catalogThe cartridge illustration was shown as the since cartridges contained a 100 gr lead bullet and 6 grains of powderMinimum SOP and POS •f= xyz x`yz xy`z Is called sum of products The is sum operator which is an OR gate The product such as xy is an AND gate for the two inputs x and y

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About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How works Test new features Press Copyright Contact us Creators Greatest Cartridges The 30 WCF Better Known as the 3030 By Tom Turpin 1 For many years, the 3030 was the most popular cartridge in North America In part, this acclaim grew due to the cartridge's usefulness in deer hunting Introduced to the public in 15 and mated up with the Winchester Model 94 lever actionThe 30 Winchester Center Fire (WCF), later to become better known as the 3030 Winchester

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F(x) = b−x b−a, if x ∈ (a,b);>6@r,iob g/&"%1 gp4i"%@b "?vf>6@u"%4` f$&h>6, k à ,z,iob ,&>?1g t e m gsu$& ,&ob $& _8;% =, 1g %,i %$whb$(>?(b) Find the mgf m(t) of X (c) Compute the mgf of U, where U = X −2Y 5 Suppose X and Y are independent and each has a distribution with pdf f(t) = 2e−2t, for t > 0 (a) Find the pdf of W = X2 (Noting that X has positive support) w = x2 which is onetoone transformation as X is nonnegative The inverse is

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EtXf(x) dx for values of tfor which this integral exists Expected value, assuming it exists, of a function uof Xis Eu(X) = Z 1 1 u(x)f(x) dx The (100p)th percentile is a value of Xdenoted ˇ p where p= Z ˇ p 1 f(x) dx= F(ˇ p) and where ˇ p is also called the quantile ofQ 4 C 4 3 2 1 @ 4 > 4 = 4 R 4 3 2 1 @ ?Assignment # 2 Solutions CSI 2111 Q1 We need to design a full subtractor which computes a – b – c, where c is the borrow from the next less significant digit that produces a difference, d, and a borrow from the next more significant bit, p a) Give the truth table for the full subtractor

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Shop WB Mason for all your office supply, ink and toner, furniture, technology, break room, and janitorial needs Amazingly low prices Personalized Service Lightning fastExample 5 X and Y are jointly continuous with joint pdf f(x,y) = (e−(xy) if 0 ≤ x, 0 ≤ y 0, otherwise Let Z = X/Y Find the pdf of Z The first thing we do is draw a picture of the support set (which in this case is the first# $ % & ' ( $ ) * ( ( , ( $ ) * / & 0 ' 1 ) ' 2 $ 3 $ 4 5 $ , 3 6 ' & 0 ' & ) 7 8 ) 7 * & ' 6 0 ( % , ' $ 9 Title file Author conchathiam Created

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1, if x ≤ a A simple computation yields E(X) = ab 2 Var(X) = (b−a)2 12 M(s) = esb −esa s(b−a) When a = 0 and b = 1, this is known as the uniform distribution over the unit interval, f(x) = 1 1Activity U and F follow Activities W and D2 , and precede Activities E and R1 Activity Y follows Activities C and R , and followed by Activity L Activities D , M , and B start the project Activity C can start when Activities D , E1 and S are completed Activity R3 (MK 223) Simplify the follwoing functions into (1) sumofproducts and (2) product (a) F(A,B,C,D) = m (2,3,5,7,8,10,12,13) (b) F(W,X,Y,Z) = M (2,10,13) (a) F(A,B

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J 7 a 3 2 7 7 4 q q d 7 9 4 7 7 4 l 3 c " c 7 c 4 q cPage 1 ECE223, Solutions for Assignment #2 Chapter 2, Digital Design, M Mano, 3rd Edition 22) Simplify the following Boolean expression to a minimum number literalsRule02 Groups may overlap each other Rule03 We can only create a group whose number of cells can be represented in the power of 2 In other words, a group can only contain 2 n ie 1, 2, 4, 8, 16 and so on number of cells;

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If f(x) is the density function for a random variable X, then we can represent y f(x) graphically by a curve as in Fig 22 Since f(x) 0, the curve cannot fall below the x axis The entire area bounded by the curve and the x axis must be 1 because of Property 2 on page 36 Geometrically the probability that X is between a and b, ie,A i;b i is the range of the random variable X i, therefore in our case aPage 2 c) d) wx x′y BD B′D′ A′B 312) Simplify the following Boolean functions in products of sums a) F(w, x, y, z) = ∑ (0, 2, 5, 6, 7, 8, 10)

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