3. Evaluate the following payoffs for the game pictured here: (a) ui(οι, Γ) for σ,-(ja, 1/4, 1/4, 1/4) (b) 112(oi, О) for σ,-(1/8, î/4, 1/43/8) 2 OA | 2,2 | 2,2 2,2 2, IA 4,2 1,3 IB 3,4 1,3
Problem 4.9 (e) /(z) = and γ is parametrized by r(t), 0 z + t 1, and satisfies Imr(t)> 0, r(0) -4 + i, and γ(1) 6 + 2i (f) f(s) sin(z) and γ is some piecewise smooth path from 1 to π. 4.2 and the fact that the length of γ does not change under 4.9. Prove Proposi reparametrization. (Hint: Assume γ, σ, and τ are smooth. Start with the definition off, f, apply the chain rule to σ...
9. Let X and Y be two random variables. Suppose that σ = 4, and σ -9. If we know that the two random variables Z-2X?Y and W = X + Y are independent, find Cov(X, Y) and ρ(X,Y). 10. Let X and Y be bivariate normal random variables with parameters μェー0, σ, 1,Hy- 1, ơv = 2, and ρ = _ .5. Find P(X + 2Y < 3) . Find Cov(X-Y, X + 2Y) 11. Let X and Y...
1.)Find dy for the given values of x and Δx. y=6x5−9x; x=−3 and Δx=0.1 dy= 2.) calculas
3 [15 pts Consider the Lorenz system given by xy-B2, z = where σ, ρ, β > 0 are constants. For ρ (0.1), using the Lyapunov function V(x, y, z) = ρ「2 + ơy2 + ơz?, show that the origin is globally asymptotically stable. (Hint. You may need to use the Invariance Principle as well.) στ 3 [15 pts Consider the Lorenz system given by xy-B2, z = where σ, ρ, β > 0 are constants. For ρ (0.1), using...
Question 4 The correct IUPAC name for the following compound is A. 2,3-Dimethyl-4-propyl-5-hexene 4,5-Dimethyl-3-propyl-1-hexene c. 2,3-Dimethyl-4-isopropyl-5-hexene D. 4,5-Dimethyl-3-propyl-2-hexene
l A. 1, 4, 2,3 B. 1, 4, 3,2 C. 4, 3, 2,1 D. 4,1, 2,3 (E)2, 3, 4, 1 8 For which cycle in Fig. 18-27, traversed clockwise, is (a) W greater and (b) O greater? A. A 1, b2 B. A. 2, b 1 C, A, 1 b, 1 D. A. 2, b 2 a Stcinos 4 and R have identical Teneths and linear densities, but
And calculate Γ(3) and Γ(4) 24. Use substitution in such a way that the resulting integral will be a definite integral. In parts (b) and (c), evaluate the resulting definite integral. (This process will be useful when computing improper integrals numerically.) po 1 J2 1 + x4 dx 1 (b) %o (1 + x232 dx 7 dx J. 3 - 4 be (See Exercise 10(f).)
Consider machine M (Q. Σ , Γ, δ, q1, qaccept, qreject), where Q ,{qi, q2, gs, qaccept, qreject}, Σ as follows: { 0.1 } , Γ { 0.1 U } , and the transition function δ is δ (qi. Ú)-(qreject, U, R) δ (qi, 0)-(P-0, R) -(Gaccept, Prove that M is NOT a decider Describe in mathematical terms the language A that M recognises, and verify 1. your answer, ie prove that A- L(M) Consider machine M (Q. Σ ,...
"an Question 4 (4pts) Find the radius and interval of convergence of the Σ n(r 3 "an Question 4 (4pts) Find the radius and interval of convergence of the Σ n(r 3