http://www.phys.ufl.edu/courses/phy2049/old_exams/2012s/exam1sol.pdf WebDec 24, 2024 · STA 711 Week 5 R L Wolpert Theorem 1 (Jensen’s Inequality) Let ϕ be a convex function on R and let X ∈ L1 be integrable. Then ϕ E[X]≤ E ϕ(X) One proof with a nice geometric feel relies on finding a tangent line to the graph of ϕ at the point µ = E[X].To start, note by convexity that for any a < b < c, ϕ(b) lies below the value at x = b of the …

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WebAlgebra. Graph x=-1. x = −1 x = - 1. Since x = −1 x = - 1 is a vertical line, there is no y-intercept and the slope is undefined. Slope: Undefined. y-intercept: No y-intercept. Find two points on the line. x y −1 0 −1 1 x y - 1 0 - 1 1. Graph the line using the slope, y … Webminimize x2 +1 subject to (x−2)(x−4) ≤ 0, with variable x ∈ R. (a) Analysis of primal problem. Give the feasible set, the optimal value, and the optimal solution. (b) Lagrangian and dual function. Plot the objective x2 + 1 versus x. On the same plot, show the feasible set, optimal point and value, and plot the Lagrangian. Solution.. WebThe electric field in a region of space is E x = 5000x V/m, where x is in meters. a. Graph E x versus x over the region -1 m ≤ x ≤ 1 m. b. Find an expression for the potential V at … lady macbeth showing guilt quotes