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.
if x1= Acos(wt+a) and x2+ Bcos(wt+b), how can I show that
x1+x2=C cos (wt+c)? Furthermore how can I express the value of C
and c? (using complex exponentials)
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 the data, determine whether the model using (x1, x2, x3,
x4) to predict y is sufficient, or should some or all other
predictors be considered? Write the full and reduced models, and
then perform the test. Show your work and state your conclusion,
but you do not need to specify your hypothesis statements.
y 60323 61122 60171 61187 63221 63639 64989 63761 66019 67857
68169 66513 68655 69564 69331 70551
x1 83 88.5 88.2 89.5 96.2 98.1 99 100...
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 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
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.