For each of the following functions, does a constant c > 0 exist such that the...

For each of the following functions, does a constant c > 0 exist such that the function is a joint probability density function?

If yes, what is c? If not, why not?

Part (a) gives 2 points, parts (b)–(d) give each one point.

(a) f(x, y) = ( cxye −x−2y if x ≥ 0 and y ≥ 0, 0 otherwise.

(b) f(x, y) = ( cxye −x−2y if x ≥ −1 and y ≥ 1, 0 otherwise.

(c) f(x, y) = ( e −cxy if x ≥ 0 and y ≥ 1, 0 otherwise.

(d) f(x, y) = ( 1 y e −cxy if x ≥ 0 and y ≥ 1, 0 otherwise.

Expert Solution

orchestra answered 1 year ago

Which of the following does not exist?

Which of the following does not exist? (A) XeOF4. (B) NeF2. (C) XeF2. (D) XeF6.

(12%) For the following 4 functions, check if you can calculate a constant c so that...

(12%) For the following 4 functions, check if you can calculate a constant c so that the function is a PDF over the whole plane or state that such c does not exist and the corresponding function is not a PDF (state the reason for that). Note the signs of the coefficients of x2 and y2 are all different). You do not have to calculate the constant c; just provide reasoning for if that exists or not. f(x, y) =...

For each of the following production functions, determine whether it exhibits increasing, constant or decreasing returns...

For each of the following production functions, determine whether it exhibits increasing, constant or decreasing returns to scale: a) Q = K + L b) Q = L + L/K c) Q = Min(2K,2L) d) Q = (L5 )(K5)

A metal rod at 38°C is placed in a room at a constant temperature of 0°C....

A metal rod at 38°C is placed in a room at a constant temperature of 0°C. (a) If after 20 minutes the temperature of the rod is 20°C, find the temperature function T(t) that models the temperature T of the rod at time t. Assume Newton's Law of Cooling. Note: You must state the differential equation that models this situation and include how to solve this DE as part of your solution. (b)Determine the time it will take for the...

1. Functions of money and barter Consider an economy in which money does not exist, so...

1. Functions of money and barter Consider an economy in which money does not exist, so that agents rely on barter to carry out transactions. When the economy was small, barter seemed sufficient. However, the economy has now begun to grow. If people in this economy trade three goods, the price tag of each good must list ______________? prices, and the economy requires____________? prices for people to carry out transactions.Suppose that the number of goods people trade increases to 15....

Does a continuous random variable X exist with E(X − a) = 0, where a is...

Does a continuous random variable X exist with E(X − a) = 0, where a is the day of your birthdate? If yes, give an example for its probability density function. If no, give an explanation. (b) Does a continuous random variable Y exist with E (Y − b) 2 = 0, where b is the month of your birthdate? If yes, give an example for its probability density function. If no, give an explanation.

Do each of the following production functions exhibit decreasing, constant or increasing returns to scale? Prove...

Do each of the following production functions exhibit decreasing, constant or increasing returns to scale? Prove your answers. • Q = .5L.34 + K.34 • Q = [min (K, 2L)]2 • Q = (0.3L.5 + 0.7K.5)2 • Q = 4KLM where K, L, M are inputs

3. Do each of the following production functions exhibit decreasing, constant or increasing returns to scale?...

3. Do each of the following production functions exhibit decreasing, constant or increasing returns to scale? Prove your answers. • Q = .5L^.34 + K^.34 • Q = [min (K, 2L)]^2 • Q = (0.3L^.5 + 0.7K^.5)^2 • Q = 4KLM where K, L, M are inputs

Show whether each of the following production functions exhibit increasing, decreasing or constant returns to scale....

Show whether each of the following production functions exhibit increasing, decreasing or constant returns to scale. Q = 0.5KL [2.5 Marks] Q = 2K + 3L [2.5 Marks] A firm has the following production function Q = 2(XY) 0.5 Where, X is maize and Y is rice. The cost of maize is K10 and the cost of rice Is K40. The firm has a budget of K80 to spend on the two goods. Formulate the firms’ optimization problem. [5...

The following data are obtained at 0°C in a constant-volume batch reactor using pure gaseous Time,...

The following data are obtained at 0°C in a constant-volume batch reactor using pure gaseous Time, min 0 2 4 6 8 10 12 14 ∞ Partial pressure of A, mm Hg 760 600 475 390 320 275 240 215 150 The stoichiometry of the decomposition is A → 2.5 R. Find a rate equation which satisfactorily represents this decomposition.

Question