Question
In: Statistics and Probability
Prove E(X1 + X2 | Y=y) = E(X1 | Y=y) + E(X2 |Y=y). Prove both cases...
Prove E(X1 + X2 | Y=y) = E(X1 | Y=y) + E(X2 |Y=y). Prove both cases where all random variables are discrete and also when all random variables are continuous.
Solutions
orchestra answered 2 years agoRelated Solutions
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...
Case Y X1 X2
Case
Y
X1
X2
X3
X4
X5
X6
1
43
45
92
61
39
30
51
2
63
47
73
63
54
51
64
3
71
48
86
76
69
68
70
4
61
35
84
54
47
45
63
5
81
47
83
71
66
56
78
6
43
34
49
54
44
49
55
7
58
35
68
66
56
42
67
8
74
41
66
70
53
50...
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?
(1) z=ln(x^2+y^2), y=e^x. find ∂z/∂x and dz/dx. (2) f(x1, x2, x3) = x1^2*x2+3sqrt(x3), x1 = sqrt(x3),...
(1) z=ln(x^2+y^2), y=e^x. find ∂z/∂x and dz/dx.
(2) f(x1, x2, x3) = x1^2*x2+3sqrt(x3), x1 = sqrt(x3), x2 = lnx3.
find ∂f/∂x3, and df/dx3.
Consider E(Y|X1 X2) = β0 + β1X1 + β2X2. Interpret β2. Group of answer choices a....
Consider E(Y|X1 X2) = β0 +
β1X1 + β2X2. Interpret
β2.
Group of answer choices
a. It is the value of X2, on average, when
X1 = 0.
b. It is the change in the response, on average, for every unit
increase in X2, when X1 is fixed.
c. It is the change in the response, on average, for every unit
increase in X2.
d. It is the change in X2, on average, for every unit
increase in X1, holding...
For the table below, if Y is the dependent variable and X1 and X2 are the...
For the table below, if Y is the dependent variable and X1 and
X2 are the independent variables. Using the linear regression
equation Y=-0.45X1-1.34X2+15.67, which observation
has the largest absolute residual?
Observation number
Actual Y
x1
X2
1
4.5
6.8
6.1
2
3.7
8.5
5.1
3
5
9
5
4
5.1
6.9
5.4
5
7
8
4
6
5.7
8.4
5.4
The first observation
The third observation
The fifth observation
The second observation
For the table below, if Y is the dependent variable and X1 and X2 are the...
For the table below, if Y is the dependent variable and X1 and
X2 are the independent variables. Using the linear regression
equation Y=-0.45X1-1.34X2+15.67, find the Sum of
Squared Residuals? (choose the best answer)
Observation number
Actual Y
x1
X2
1
4.5
6.8
6.1
2
3.7
8.5
5.1
3
5
9
5
4
5.1
6.9
5.4
5
7
8
4
6
5.7
8.4
5.4
2.57
2.97
3.2
3.5
A detailed answer will be appreciate. 6. To prove that for all x1, x2, ..., x9...
A detailed answer will be appreciate.
6. To prove that for all x1, x2, ..., x9 ∈ {0, 1, 2, 3, 4, 5, 6,
7, 8, 9, 10}, there exists a
value of x10 for the check digit in the code ISBN-10.
7. To prove that for every x1, x2, ..., x12 ∈ {0, 1, 2, 3, 4, 5,
6, 7, 8, 9, 10}, there exists a
value of x13 for the check digit in the code ISBN-13.
1. Let ρ: R2 ×R2 →R be given by ρ((x1,y1),(x2,y2)) = |x1 −x2|+|y1 −y2|. (a) Prove...
1. Let ρ: R2 ×R2 →R be given by ρ((x1,y1),(x2,y2)) = |x1
−x2|+|y1 −y2|.
(a) Prove that (R2,ρ) is a metric space.
(b) In (R2,ρ), sketch the open ball with center (0,0) and radius
1. 2. Let {xn} be a sequence in a metric space (X,ρ). Prove that if
xn → a and xn → b for some a,b ∈ X, then a = b.
3. (Optional) Let (C[a,b],ρ) be the metric space discussed in
example 10.6 on page 344...
Let U = {(x1,x2,x3,x4) ∈F4 | 2x1 = x3, x1 + x4 = 0}. (a) Prove...
Let U = {(x1,x2,x3,x4) ∈F4 | 2x1 = x3, x1 + x4 = 0}.
(a) Prove that U is a subspace of F4.
(b) Find a basis for U and prove that dimU = 2.
(c) Complete the basis for U in (b) to a basis of F4.
(d) Find an explicit isomorphism T : U →F2.
(e) Let T as in part (d). Find a linear map S: F4 →F2 such that
S(u) = T(u) for all u ∈...
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