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Let (z1,22)-(18,4) and (yi,Y2) = (20,6) be two consumption bundles. Given ? E (0,1). the vector...
Please answer this question in both mathematically and with R. I
need R code also.. Its urgent...
3.14 For the variables in Table 3.4, define z 3y1 y2 2y3 (3,-1,2)y. Find z and sz in two ways: (a) Evaluate z for each row of Table 3.4 and find Z and s directly from 21,22,., 210 using (3.1) and (3.5). (b) Use za'y and s2- a'Sa, as in (3.54) and (3.55). The sample mean of a random sample of n observations...
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...
Let S denote the sphere x2 y2 2 = 1. Given two points P(1,0,0), (a) Find the distance between P and Q. Lets call this Euclidean distance. (b) Find the plane that goes through O, P, Q. What is the intersection of this plane with the sphere? (Hint: use OP × OQ as the the normal vector) (c) Observe that the length of the arc PQ is 0 the angle between OP,0Q in radians. (Hint: You know how to find...