(1 point) Let u= (3, 2) and v = (1,5). Then u +v=< 7 U-v=< -30 =< u. V = and || 0 ||
12) Let U ={NEN:n <200} , find the number of elements of U that are divisible by 2, 3, or 7.
PROB5 Let U and V be independent r.v's such that the p.d.f of U is fu(u) = { 2 OSU< 27, otherwise. and the p.d.f'of2 is Seu, v>0, fv (v otherwise. Let X = V2V cos U and Y = 2V sin U. Show that X and Y are independent standard normal variables N(0,1).
(1 point) Let u = (-2,-3) and v = (-1,6). Then u+v=< >, u-v=< -3v=< u.V= and || 0 ||
Qi. Let x be a real number and u, v be the vectors u =< x,-V3x >, v =< -x,-3 > a) Find the value(s) of x if u.v 6 b) Let x v3, find the angle between the vectors u and v
5-1. Let U - Uniform(0,1) and X = - In(1-U). Show that the CDF of X is Fx(x) = 1 -e*, 0<x<0 In other word, X is exponentially distributed with 1 = 1.
5-1. Let U ~ Uniform(0,1) and X = – ln(1 – U). Show that The CDF of X is Fx(x) = 1 – e-X, 0 < x < 0 In other word, X is exponentially distributed with 2 = 1.
w Find the exact value of the trigonometric expression given than sin u = - where 3 < <u<2nt and cos v = - 15, where 0 < v cos(u - v)
7. Let u =< 2,0,3 > and v =< -1,1,0 > (a) Find || 11 (b) Find u-2u.
Question 34 In the exercise below, let U = {x|XE N and x < 10} A = {x|x is an odd natural number and x < 10} B = {x|x is an even natural number and x < 10} C = {x|x € N and 3 <x<5} Find the set. Во С {4} {1, 2, 3, 4, 5, 6, 7, 8, 9} {2, 4, 6, 8, 10} {1, 2, 3, 4, 5, 6, 7, 8, 9, 10)