Question

Set theory proof:

Rearrange: (A U B) X (C U D) to equal (A X C) U (B X D)

I get stuck after the following steps:

1. (x,y) exist (A U B) X (C U D)

2. x exist (A U B) X y exist (C U D)

3. (x exist A OR x exist B) AND (y exist C OR y exist D)

I know that somehow we can get to but I need it explained:

4. (x exist A AND y exist C) OR (x exist B AND y exist D)

I need a full explanation of how we can get from step 3 to 4.

Answer #1

x ∈ A means x belongs to A

a) U = xy
b) U = (xy)^1/3
c) U = min(x,y/2)
d) U = 2x + 3y
e) U = x^2 y^2 + xy
2. All homogeneous utility functions are homothetic. Are any of
the above
functions homothetic but not homogeneous? Show your work.

A subset of a power set.
(a)
Let X = {a, b, c, d}. What is { A: A ∈ P(X) and |A| = 2 }?
comment: Please give a clear explanation to what this
set builder notation translate to? Because I've checked the answer
for a) and it is A= {{a,b}, {a,c}, {a,d}, {b,c}, {b,d},
{c,d}}.
I don't understand because the
cardinality of A has to be 2 right? Meanwhile, the answer is
basically saying there's 6 elements. So...

Given
ID
X
Y
A
10
15
B
4
5
C
13
16
D
7
9
E
13
4
F
1
5
What is the variation in Y that can be explained by X? please
explain
A) 50.7
B) 22.7
C) 36.3
D) 105.7
E) 91.3

Let (X, d) be a metric space, and let U denote the set of all
uniformly continuous functions from X into R. (a) If f,g ∈ U and we
define (f + g) : X → R by (f + g)(x) = f(x) + g(x) for all x in X,
show that f+g∈U. In words,U is a vector space over R. (b)If f,g∈U
and we define (fg) : X → R by (fg)(x) = f(x)g(x) for all x in X,...

Model: Y = β0 + β1X + u If E(u|X) 6= 0, then we know the OLS
estimator will be biased and all further inference like Hypothesis
test and Confidence interval will be invalid. In presence of such
violation, we can go to Instrument variable estimation/regression
method to rebuild the valid empirical study. Assume there is a
“good” instrument variable Z for X. (1) How would you argue this is
a valid instrument variable?(Hint: validity condition and relevance
condition) (2)...

Model: Y = β0 + β1X + u If E(u|X) 6= 0, then we know the OLS
estimator will be biased and all further inference like Hypothesis
test and Confidence interval will be invalid. In presence of such
violation, we can go to Instrument variable estimation/regression
method to rebuild the valid empirical study. Assume there is a
“good” instrument variable Z for X. (1) How would you argue this is
a valid instrument variable?(Hint: validity condition and relevance
condition) (2)...

A potential energy function is given by U(x) = x^(−8)e^x^2 .
Let’s only focus on the region where x > 0.
a) Find the position where the potential energy is a minimum
b) For small oscillations around this minimum, what is the
angular frequency ω?
c) At what distance (either to the left or right) from the
equilibrium point is the exact value of the force (derived from the
full potential) more than 10% different from the force
corresponding to...

Id
x
z
y
A
6
7
3
B
4
4
7
C
10
10
8
D
3
1
4
E
2
3
2
given
Ryx= 0.6719
Ryz=0.5190
ssy=26.8
1. what is the variation in y that is redundantly explained by x
and z
2. What is the proportion of variation in y that is redundantly
explained by x and z

Given the following information on Events A, B, C, and D.
P(A) = 0.35
P(A U D) = 0.55
P(A n D) = 0.12
P(B) = 0.18
P(A I B) = 0.43
P(C) = 0.25
P(A n C) = 0.07
1.Compute P(D).
2.Compute P(A n B).
3.Compute P(A I C).
4.Compute the probability of the complement of C
5. Are events A and C independent? Explain.

combinations
X
Y
A
10
10
B
12
12
C
10
8
D
8
12
can we conclude that
(a) B>A?
(b)D>A?
(c) if D>A, then D>C?
Explain please.
I believe this relates to indifference curves. This is a
chart of consumer preferences.

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