Question

There are two error terms e1 and e2.

- E[e1]=E[e2]=0

- e1 and e2 are independent

- E[e2-e1 | e2 -e1 < a ] and E[e2-e1 | e2 - e1 > a] are not 0.

**Q: Can we say E[e1 | e2-e1 < a ] = E[ e2 | e2-e1 >
a ] = 0? Why? ( a is just a constant )**

Answer #1

how the probability of P(E1 ∪ E2) = P(E1) + P(E2)−P(E1 ∩
E2).
we know that E1 union E2 = P(E1)+P(E2) (or) but why we do have
−P(E1 ∩ E2). at the end of the equation above
thank you in advanced

Prove or give a counter example for "If E1 and
E2 are independent, then they are conditionally
independent given F."

In a gum can have two food colors: food color E1 and food color
E2. The chance of having type E1 edible paint gum is 0.8. The
chance of having a type E2 edible color gum is 0.7. Food colors of
both types are known to be independent of each other. Randomly
selected gum. What is the probability of having exactly one food
color (of the two types)?
A. 0.404
B. 0.38
C. 0.94
D. 0.595
?

In this question, as usual, e1, e2, e3 are the standard basis
vectors for R 3 (that is, ej has a 1 in the jth position, and has 0
everywhere else). (a) Suppose that D is a 3 × 3 diagonal matrix.
Show that e1, e2, e3 are eigenvectors of D. (b) Suppose that A is a
3 × 3 matrix, and that e1, e2, and e3 are eigenvectors of A. Is it
true that A must be a diagonal...

Determine the resultant of the two waves E1 = 4.00 sin(100 πt)
and E2 = 7.80 sin(100 πt + π/2).
E1 + E2 =

in an inertial frame, two events
E1 and E2 are separated by a distance 6 m in the x-direction. E1
occurs 4.0 s before event E2. An observer in inertial frame S'
moving in the x-direction relative to frame S observes the events
at the same location. what time interval does frane S' observe
between the events?

Find the coordinates of e1 e2
e3 of R3 in terms of [(1,0,0)T ,
(1,1,0)T , (1,1,1)T ] of R3,, and
then find the matrix of the linear transformation T(x1,,
x2 , x3 )T = [(4xx+
x2- x3)T , (x1 +
3x3)T , (x2 +
2x3)T with respect to this basis.

Consider the following equations:
y1 = a1y2 +a2y3 +x1 +x2 +e1 (1) y2 = by1+2x3+x1+e2 (2) y3 =cy1+e3
(3)
Here a1, a2, b, c are unknown parameters of interest, which are all
posi- tive. x1, x2, x3 are exogenous variables (uncorrelated with
y1, y2 or y3). e1, e2, e3 are error terms.
(a) In equation (1), why y2,y3 are endogenous?
(b) what is (are) the instrumental variable(s) for y2, y3 in
equation (1)?
(no need to explain why)
(c) In...

Suppose that we have a sample space with five equally likely
experimental outcomes: E1, E2, E3, E4, E5. let
a = {E1, E2}
B = {E3, E4}
C = {E2, E3, E5}
a. Find P(a), P(B), and P(C).
b. Find P(a ∙ B). Are a and B mutually exclusive?
c. Find ac, Cc, P(ac), and P(Cc).
d. Finda∙Bc andP(a∙Bc).
e. Find P(B ∙ C ).

?-ketogluterate dehydrogenase and pyruvate dehydrogenase
catalyze similar reactions using the same reaction mechanisms. E1
and E2 of the two enzyme complexes share a lot of similarities,
however they are not identical. The E3 enzyme of the two enzyme
complexes are identical. Keeping the functions of each of the three
enzymes in mind, explain why it makes sense that the E1/E2 enzymes
are only similar, whereas the E3 enzymes are identical.

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