1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Maslowich
3 years ago
10

If s is an increasing function, and t is a decreasing function, find Cs(X),t(Y ) in terms of CX,Y .

Mathematics
1 answer:
Sedbober [7]3 years ago
7 0

Answer:

C(X,Y)(a,b)=1−C(s(X),t(Y))(a,1−b).

Step-by-step explanation:

Let's introduce the cumulative distribution of (X,Y), X and Y :

F(X,Y)(x,y)=P(X≤x,Y≤y)

  • FX(x)=P(X≤x)
  • FY(y)=P(Y≤y).

Likewise for (s(X),t(Y)), s(X) and t(Y) :

F(s(X),t(Y))(u,v)=P(s(X)≤u

  • t(Y)≤v)
  • Fs(X)(u)=P(s(X)≤u)
  • Ft(Y)(v)=P(t(Y)≤v).

Now, First establish the relationship between F(X,Y) and F(s(X),t(Y)) :

F(X,Y)(x,y)=P(X≤x,Y≤y)=P(s(X)≤s(x),t(Y)≥t(y))

The last step is obtained by applying the functions s and t since s preserves order and t reverses it.

This can be further transformed into

F(X,Y)(x,y)=1−P(s(X)≤s(x),t(Y)≤t(y))=1−F(s(X),t(Y))(s(x),t(y))

Since our random variables are continuous, we assume that the difference between t(Y)≤t(y) and t(Y)<t(y)) is just a set of zero measure.

Now, to transform this into a statement about copulas, note that

C(X,Y)(a,b)=F(X,Y)(F−1X(a), F−1Y(b))

Thus, plugging x=F−1X(a) and y=F−1Y(b) into our previous formula,

we get

F(X,Y)(F−1X(a),F−1Y(b))=1−F(s(X),t(Y))(s(F−1X(a)),t(F−1Y(b)))

The left hand side is the copula C(X,Y), the right hand side still needs some work.

Note that

Fs(X)(s(F−1X(a)))=P(s(X)≤s(F−1X(a)))=P(X≤F−1X(a))=FX(F−1X(a))=a

and likewise

Ft(Y)(s(F−1Y(b)))=P(t(Y)≤t(F−1Y(b)))=P(Y≥F−1Y(b))=1−FY(F−1Y(b))=1−b

Combining all results we obtain for the relationship between the copulas

C(X,Y)(a,b)=1−C(s(X),t(Y))(a,1−b).

You might be interested in
A transformation T : (x, y) → (x + 3, y + 1). Find the preimage of the point (4, 3) under the given transformation. (7, 4) (1, 2
motikmotik

Answer:

(1, 2)

Step-by-step explanation:

Remember that the final shape and position of a figure after a transformation is called the image, and the original shape and position of the figure is the pre-image.

In our case, our figure is just a point. We know that after the transformation T : (x, y) → (x + 3, y + 1), our image has coordinates (4, 3).

The transformation rule T : (x, y) → (x + 3, y + 1) means that we add 3 to the x-coordinate and add 1 to the y-coordinate of our pre-image. Now to find the pre-image of our point, we just need to reverse those operations; in other words, we will subtract 3 from the x-coordinate and subtract 1 from the y-coordinate.

So, our rule to find the pre-image of the point (4, 3) is:

T : (x, y) → (x - 3, y - 1)

We know that the x-coordinate of our image is 4 and its y-coordinate is 3.

Replacing values:

                (4 - 3, 3 - 1)

                (1, 2)

We can conclude that our pre-image is the point (1, 2).

6 0
2 years ago
Find the value of X in the simplest radical form
Galina-37 [17]

Answer:. 7


Step-by-step explanation:


4 0
2 years ago
ASAP!!! help its emergent​
Bezzdna [24]

Answer:

Step-by-step explanation:

F(x)=(5 t^2+t  )x to x+3

=5((x+3)^2-x^2)+(x+3-x)

=5(x^2+6x+9-x^2)+3

=5 (6x+9)+3

=30x+48

F'(x)=30

3 0
3 years ago
The Central Limit Theorem tells us that for population distribution(s), if we repeatedly take new random samples from this distr
sertanlavr [38]

Answer:

d. If your sample size is very large, the distribution of the sample averages will look more like distribution.

Step-by-step explanation:

The central limit Theorem states that for population distribution if you repeatedly take samples from the distribution, then the normal thing for it to happen would be that the distribution means of the samples will be normally distributed, this is what it states, the option that comes closer to that statement would be  d. If your sample size is very large, the distribution of the sample averages will look more like distribution, because they large sample will create for a normally distributed means distribution.

7 0
3 years ago
Which is a factor of x^2-9x+14?<br> A. X-9<br> B. X-2<br> C. X+5<br> D. X+7
sukhopar [10]

Answer : B

x^2-9x+14

Lets factor x^2-9x+14

We find out two factors whose product is +14 and sum is -9

Two factors are -2  and -7, we split the middle term -9x using -2  and -7

x^2-2x-7x+14

Group first two terms and last two terms

Then factor out GCF from each term

(x^2-2x)(-7x+14)

x(x-2)-7(x-2)

(x-2)(x-7)

so x-2 is one of the factor

3 0
3 years ago
Other questions:
  • Please help quickly needed !<br> thank you !
    12·1 answer
  • The ratio of long boards to short boards is 4 to
    10·2 answers
  • PLEASE HELP =(
    11·1 answer
  • 2) Jimmy was going to sell all of his stamp
    9·1 answer
  • Add and turn to simplest form.
    14·2 answers
  • T(t)T, models the daily high temperature (in Celsius) in Santiago, Chile, t days after the hottest day of the year. Here, t is e
    7·1 answer
  • A car drives 40 miles on local roads at 20 mph, and 180 miles on the highway at 60 mph, w Your dinner bill is $25 before tax. Th
    5·1 answer
  • If 3x+5=11 what is the value of x-2
    7·1 answer
  • PLEASE HELP!! I WILL GIVE BRAINLIEST
    8·1 answer
  • A square room has a floor area of 25 meters. the height is 3 meters what is the area of one wall
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!