COS X Objective is to prove that log' x is improperly integrable on le,c).
21. Is the following function continuous at (0,0)? Hint:lim 1-cos T (1-cos(x2 +y2) f(x, y)=11-cosztym if(x,y) (0,0) if (x,y) = (0,0)
15. lim xy cos y (x, y)+(0,0) x2 + y4
An individual has the utility function: U(x1,x2,x3) = ln x1 + ln x2 + 0.5ln x3. The price of good x1 is p1, the price of good x2 is p2 = 1 and the price of good x3 is p3. The individual’s income is I. Derive the Marshallian demand functions (x1* , x2*, x3* ).
x?sin’y If the function f(x y)= { x2 +2V2' (x,y) (0,0) is continuous at (0,0), then (x y) = (0,0) AK) Ox= 1/2 0-1 .k=0 ok=2 ok=1
= = 3, Cov(X1, X2) = 2, Cov(X2, X3) = -2, Let Var(X1) = Var(X3) = 2, Var(X2) Cov(X1, X3) = -1. i) Suppose Y1 = X1 - X2. Find Var(Y1). ii) Suppose Y2 = X1 – 2X2 – X3. Find Var(Y2) and Cov(Yı, Y2). Assuming that (X1, X2, X3) are multivariate normal, with mean 0 and covariances as specified above, find the joint density function fxı,Y,(y1, y2). iii) Suppose Y3 = X1 + X2 + X3. Compute the covariance...
Let (X1,X2,X3) have the joint pdf fx(x1, x2, x3) = k*x1*x2*x3; 0 < x1 < x2 < x3 < 1. Consider the transformation U1 = X1/X2; U2 = X2/X3; U3 = X3. a) Find the value of k. b) Find the joint pdf fu(u1, u2, u3) of U1,U2,U3.
determine whether or not the equations represent y as a function of x y=x3-X X2-Y2=1 X3+Y3=4
Let X1, X2, and X3 be a random sample from a discrete distribution with probability function g(x) =x/10 for x= 1, 2, 3, 4 and g(x) = 0 otherwise. What is P(X1< X2< X3)?
1. [10 marks) Let X, and X, have joint density function f(0,0%) = cca 110, x2 > 0,8 +29 < 1, where c is a constant. Find: (a) (2 marksThe value of c. (b) (2 marks] E(XX). (c) (2 marks] P(X1 < 3X2). (a) (2 marks] (2016). (e) (2 marks] E(X1/X3 = 5).