(1 point) Let u = (-2,-3) and v = (-1,6). Then u+v=< >, u-v=< -3v=< u.V= and || 0 ||
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).
Let u =
u =<4, -5 > v=<3, 2 > | 2u – vl = ? Whole number. <7, -1, 5 >.< 2, 3, 1>=? whole number
7. (1 point) Let X be the mean of a random sample of size 36 from the uniform distribution U(7,15) Find P(11.3 <X < 11.5)
12) Let U ={NEN:n <200} , find the number of elements of U that are divisible by 2, 3, or 7.
Problem 4 Suppose U and V follow uniform [0, 1] independently. (1) Let X = min( UV). Let F(x) = P(X<2). Calculate F(2) and f(c). (2) Let Y = max(U,V). Let F(y) = P(Y = y). Calculate F(y) and f(y). (3) Let Z=U + V. Let F(z) = P(Z < z). Calculate F(2) and f(z).
Question 7 Given vectors u = <2, 1> and v= <3,4> to compute (a) u + v (b) - (c) u-30
7. Let u =< 2,0,3 > and v =< -1,1,0 > (a) Find || 11 (b) Find u-2u.
Question 19: Linear Transformations Let S = {(u, v): 0 <u<1,0 <v<1} be the unit square and let RCR be the parallelogram with vertices (0,0), (2, 2), (3,-1), (5,1). a. Find a linear transformation T:R2 + R2 such that T(S) = R and T(1,0) = (2, 2). What is T(0, 1)? T(0,1): 2= y= b. Use the change of variables theorem to fill in the appropriate information: 1(4,)dA= S. ° Sºf(T(u, v)|Jac(T)| dudv JA JO A= c. If f(x, y)...