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1. Consider the Boolean function F(x, y) = x + y, how many cells in the Kmap representing this function have value of “1”? A. 3 B. 2 C. 4 D. 1 2.Using Kmap for simplification, we can select multiple smaller groups (instead of a larger group) as long as all “1” are selected. A. False B. True 3 In Kmap representation, how many values of “0” and “1” two neighboring minterms can differ?2. Using Kmap for simplification, we can...
Given f(x,y) = 2 ; 0 <X<y< 1 a. Prove that f(x,y) is a joint pdf b. Find the correlation coefficient of X and Y
1. X ~ N(mu = 3,sigma=10) Y=2X+4 E(Y) = ? 2. X ~ N(mu = 3,sigma=10) Y=2X+4 V(Y) = ? 3. If X and Y are independent then E(XY) =E(X)*E(Y) True or False? 4. If Cov(X,Y) = 0 then X and Y are independent True or False? 5. If Y_1 ~ N( 1, sigma =2) and Y_2 ~ N(-2, sigma^2 = 16) and Y_1 is independent of Y_2. If l = 2Y_1 - 3Y_2 find E(l) 6. If Y_1 ~...
Q2: 1. Proof this Boolean expression. Use Boolean Algebra (X+Y). (Z+W).(X'+Y+W) = Y.Z+X.W+Y.W 2. For this BF F(X,,Z)=((XYZ)(X +Z))(X+Y) • Design the digital circuit Derive the Boolean Function of X, Y, Z. Simplify the Function Derive the truth table before and after simplification. Derive the BF F(X,Y,Z) as Maxterms (POS) and miterms (SOP). Implement the F(X,Y,Z) after simplification using NAND gates only. Implement the F(X,Y,Z) after simplification using OR NOR gates only.
81. Consider the function g(x, y) given by, 1 1.52.53 11/4 0 0 0 2 0 1/8 0 0 y 3 0 1/4 0 0 4 0 0 1/4 0 5 00 0 1/8 and complete / determine the following: (a) Show that g(x, y) satisfies the properties of a joint pmf. (See Table in ?6.0.1.) (b) P(X < 2.5,Y < 3) (c) P(X < 2.5) (d) P(Y < 3) (e) P(X> 1.8, Y> 4.7) (f) E[X], EY], Var(X), Var(Y)...
using discrete structures 3. Consider the function F(x, y, z) for x, y, z z 0 defined as follows: a. F(x, y, 0)-y+1 b. F(x, 0, 1)-x c, F(x, 0, 2) = 0 d. F(x, 0, z+ 3)-1 e. F(x, y, z)-F(x, F(x, y-1, z), z-1) Using Induction, prove the following a. F(x, y, 1)-x +y b, F(x, y, 2) = xy c. F(x, y, 3)-xy 3. Consider the function F(x, y, z) for x, y, z z 0 defined...
Realizing the following functions using only 8-to-1 multiplexer: F_1(x, y, z) = Sigma m(0, 2, 3, 5, 7) F-(x, y, z)=y' + z
3. Let y: K + Aut(H) be a homomorphism. Write (k) = Ok. Let G be a group. A function d: K + H is called a derivation if dikk') = d(k) (d(k')). Show that d: K + H is a derivation if and only if V: K + H y K given by v(k) = (d(k), k) is a homomorphism. 4. Suppose that a: G + K is a surjective homomorphism and that 0: K + G is a...
Prove the following please, thank you. Given f(x,y) = min (3,5y). For example, f(3, 1) = min (3,5) = 3. Compute 1 f(x,y) dy dx = min (x, y) dy dx x=0 y=0
Let x and y be vertices of G such that dist(x, y) 2 2. Prove that G contains at least dist(x,y)-1 vertices z other than x and y such that dist(x,y) = dist(x, z) dist(2, y) Let x and y be vertices of G such that dist(x, y) 2 2. Prove that G contains at least dist(x,y)-1 vertices z other than x and y such that dist(x,y) = dist(x, z) dist(2, y)