Exercise 3 Consider open subsets U1 and U2 of the unit cicle Sl given by Ui...
1) In this exercise, we are given the distribution of Sn=U1+U2+…+Un, where Ui are i.i.d. Uniform(a=0,b=1) random variables. a) Find the p.d.f. of S3=U1+U2+U3 and sketch its graph. b) Find the p.d.f. of S4=U1+U2+U3+U4 and sketch its graph c) Neither S3 or S4 are distributions with a name, but if you sketch their p.d.f.s, they should resemble a previous distribution. Which one?
2 uF 10 kQ U2 U1 0 3 H U2 U1 7 H 10 uF 2 H U2 U1 0 Define for given systems Ordinary Differential Equations. Obtain State Space Model of the given systems 2 uF 10 kQ U2 U1 0 3 H U2 U1 7 H 10 uF 2 H U2 U1 0 Define for given systems Ordinary Differential Equations. Obtain State Space Model of the given systems
Exercise 3. Let u2= (5) C) V2 = V1 = and E u1, u2},F = {v1,v2} be two ordered bases for R2. Let also 5 (i) Find the coordinate vectors of [x]E and [x\f. (ii) Find the transition matrix S from the basis E to F. (ii) Verify that [x]f = S[r]E Exercise 3. Let u2= (5) C) V2 = V1 = and E u1, u2},F = {v1,v2} be two ordered bases for R2. Let also 5 (i) Find the...
Question 7 (Chapters 6-7) 2+2+2+3+2+4+4-19 mark Let 0メs c Rn and fix r' E S. For a R" consider the following optimization problem: (Pa) min ar res and define the set K(S,) (aER z" is a solution of (Pa)) (e) If z' e int(S), prove that K(S, (0) (1) If possible, find a set S CR" and s* E S such that K(S,) (g) Let SB, 0.1] (rR l2l3 1) (the closed (, unit ball) and consider (1,0)7. Prove that...
Question 8 (Chapters 6-7) 12+2+2+3+2+4+4-19 marks] Let 0メS C Rn and fix E S. For a E R consider the following optimization problem: (Pa) min a r, and define the set K(S,x*) := {a E Rn : x. is a solution of (PJ) (a) Prove that K(S,'). Hint: Check 0 (b) Prove that K(S, r*) is a cone. (c) Prove that K(S,) is convex d) Let S C S2 and fix eS. Prove that K(S2, ) cK(S, (e) Ifx. E...
Have to get an idea of how i am doing on this problem. Whould be nice to get a good explaination for each part of the problem. d1 and d2 is the two different metrics, p ,Y. Problem 2. Consider first the following definition: Definition. Let X be a set and let pand be two metrics on X. We say that p and are equivalent if the open balls in (X, p) and (x,y) are "nested". More precisely, p and...
Please do exercise 129: Exercise 128: Define r:N + N by r(n) = next(next(n)). Let f:N → N be the unique function that satisfies f(0) = 2 and f(next(n)) =r(f(n)) for all n E N. 102 1. Prove that f(3) = 8. 2. Prove that 2 <f(n) for all n E N. Exercise 129: Define r and f as in Exercise 128. Assume that x + y. Define r' = {(x,y),(y,x)}. Let g:N + {x,y} be the unique function that...
Hi, could you post solutions to the following questions. Thanks. 2. (a) Let V be a vector space on R. Give the definition of a subspace W of V 2% (b) For each of the following subsets of IR3 state whether they are subepaces of R3 or not by clearly explaining your answer. 2% 2% (c) Consider the map F : R2 → R3 defined by for any z = (zi,Z2) E R2. 3% 3% 3% 3% i. Show that...
FR #3.(30 pts): For the given line of current determine the force per unit length it would feel if a second line of current (1 = 4.56 Amperes) ran in the same direction at a distance of 0.833 m. 1 = 3.00 A If we consider the motion of a +3.33C charge (m = 2.54"?kg) being directed at the wire in the diagram below, derive the expression describing its closest approach: Xo Rs sin (8 4 then calculate its closest...