A set X is said to be closed under multiplication if for every x1,x2 ∈ X...

A set X is said to be closed under multiplication if for every x1,x2 ∈ X we have x1x2 ∈ X. Let A be the union of all bounded subsets X ⊆ R that are closed under multiplication. Does inf(A) exist? If it does, find it.

Expert Solution

Colby Messinger answered 2 years ago

The set R^2 with addition and scalar multiplication defined by (x1, y1) + (x2, y2) =...

The set R^2 with addition and scalar multiplication defined by (x1, y1) + (x2, y2) = (x1 + x2, y1 + y2) c(x1, y1) = (cx1, y1) is not a vector space. Determine which axiom fails and find a counterexample that shows that it fails.

Does the input requirement set V (y) = {(x1, x2, x3) | x1 + min {x2,...

Does the input requirement set V (y) = {(x1, x2, x3) | x1 + min {x2, x3} ≥ 3y, xi ≥ 0 ∀ i = 1, 2, 3} corresponds to a regular (closed and non-empty) input requirement set? Does the technology satisfies free disposal? Is the technology convex?

Using Matlab 1. Solve the following equations set f1 (x1,x2) = sin (sin (x1)) +x2 f2...

Using Matlab 1. Solve the following equations set f1 (x1,x2) = sin (sin (x1)) +x2 f2 (x1,x2) = x1+ e^(x2) a) Can this equation set be solved by the fixed - point method with the following expressions? And why? Show your analysis with a 2D graph. g1 (x1,x2) = -e^(x2) g2 (x1,x2) = -sin⁡(x1) b) Use Newton Raphson Method with initial values x1 = -2, x2 = 1.5. (8 significant figures. Please submit the code and results.)

If the joint probability distribution of X1 and X2 is given by: f(X1, X2) = (X1*X2)/36...

If the joint probability distribution of X1 and X2 is given by: f(X1, X2) = (X1*X2)/36 for X1 = 1, 2, 3 and X2 = 1, 2, 3, find the joint probability distribution of X1*X2 and the joint probability distribution of X1/X2.

2.2.8. Suppose X1 and X2 have the joint pdf f(x1, x2) = " e−x1 e−x2 x1...

2.2.8. Suppose X1 and X2 have the joint pdf f(x1, x2) = " e−x1 e−x2 x1 > 0, x2 > 0 0 elsewhere . For constants w1 > 0 and w2 > 0, let W = w1X1 + w2X2. (a) Show that the pdf of W is fW (w) = " 1 w1− w2 (e−w/w1 − e−w/w2) w > 0 0 elsewhere . (b) Verify that fW (w) > 0 for w > 0. (c) Note that the pdf fW...

Bridgit’s utility function is U(x1, x2)= x1 + ln x2 x1 - stamps x2 - beer...

Bridgit’s utility function is U(x1, x2)= x1 + ln x2 x1 - stamps x2 - beer Bridgit’s budget p1 x1 + p2 x2 = m p1 – price of stamps p2 – price of beer m – Bridgit’s budget a) What is Bridgit’s demand for beer and stamps? b) Is it true that Bridgit would spend every dollar in additional income on stamps? c) What happens to demand when Bridgit’s income changes (i.e. find the income elasticity)? d) What happens...

Let T(x1, x2) = (-x1 + 3x2, x1 - x2) be a transformation. a) Show that...

Let T(x1, x2) = (-x1 + 3x2, x1 - x2) be a transformation. a) Show that T is invertible. b)Find T inverse.

Consider the following three consumption bundles (X1,X2)=(10,10) ; (X1,X2)=(15,10) ; (X1,X2)=(3000,8).

Answer each of the following statements True/False/Uncertain. Give a full explanation of your answer including graphs where appropriate. (When in doubt, always include a fully labeled graph.)A) Consider the following three consumption bundles (X1,X2)=(10,10) ; (X1,X2)=(15,10) ; (X1,X2)=(3000,8). Non-satiation implies that (15,10) is preferred to (10,10) but does not imply that (3000,8) is preferred to (10,10).B) It is not theoretically possible for two indifference curves to cross if the preference relations they are based on satisfy the assumptions of completeness,...

Suppose that random variable X 0 = (X1, X2) is such that E[X 0 ] =...

Suppose that random variable X 0 = (X1, X2) is such that E[X 0 ] = (µ1, µ2) and var[X] = σ11 σ12 σ12 σ22 . (a matrix) (i) Let Y = a + bX1 + cX2. Obtain an expression for the mean and variance of Y . (ii) Let Y = a + BX where a' = (a1, a2) B = b11 b12 0 b22 (a matrix). Obtain an expression for the mean and variance of Y . (ii)...

Let X = ( X1, X2, X3, ,,,, Xn ) is iid, f(x, a, b) =...

Let X = ( X1, X2, X3, ,,,, Xn ) is iid, f(x, a, b) = 1/ab * (x/a)^{(1-b)/b} 0 <= x <= a ,,,,, b < 1 then, find a two dimensional sufficient statistic for (a, b)

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