Show that the conditional expectation ψ(x) = E(Y | X) satisfies E(ψ(X)g(x)) = E(Yg(x)), for any function g for which both expectations exist.

Answers

Answer 1

This means that for any Borel set B, we have the following

:$$\int_B\psi(X(\omega))dP(\omega) = \int_B\psi(x)dP_X(x) = \int_{X^{-1}(B)}Y(\omega)dP(\omega)$$

To verify the given question, we need to show that

E(ψ(X)g(x)) = E(Yg(x)),

for any function g for which both expectations exist.

The conditional expectation

ψ(x) = E(Y | X)

satisfies

E(ψ(X)g(x))

= E(Yg(x)),

for any function g for which both expectations exist.Let us solve the given question. Consider the random variable Y and X. Given

X=x, we define the conditional expectation as the function of

x,  ψ(x)

= E(Y | X

=x)ψ(x)

is X-measurable.

This means that for any Borel set B, we have the following:

$$\int_B\psi(X(\omega))dP(\omega)

= \int_B\psi(x)dP_X(x)

= \int_{X^{-1}(B)}Y(\omega)dP(\omega)$$

To verify the given question, we need to show that

E(ψ(X)g(x))

= E(Yg(x)),

for any function g for which both expectations exist. Let us show the verification below.

$$\begin{aligned} E(\psi(X)g(X)) &

= \int \psi(X(\omega))g(X(\omega))dP(\omega) \\ &

= \int\left(\int Y(\omega)dP(\omega)|X(\omega)

= x\right)g(x)dP_X(x) \\ &

= \int Y(\omega)\left(\int g(x)dP_{Y|X}(y|x)\right)dP(\omega) \\ &

= \int Y(\omega)g(X(\omega))dP(\omega) \\ &

= E(Yg(X)) \end{aligned}$$

Therefore, we have shown that

E(ψ(X)g(x))

= E(Yg(x)),

for any function g for which both expectations exist.

To know more about Borel visit:

https://brainly.com/question/32643019

#SPJ11


Related Questions

Sketch a graph showing the solution to each system.If you can't do both then do Question C.

Sketch a graph showing the solution to each system.If you can't do both then do Question C.

Answers

(C)

Given data:

The given inequalities.

The graph of the given inequalities is shown below.

Sketch a graph showing the solution to each system.If you can't do both then do Question C.

Why are you allowed to move the decimal points before
dividing with decimals? Explain your reasoning.

Answers

Sample Response: If you move the decimal point the same number of places in the dividend and the divisor, you are multiplying them both by the same power of 10. That does not change the quotient.

Answer: If you move the decimal point the same number of places in the dividend and the divisor, you are multiplying them both by the same power of 10. That does not change the quotient.

Step-by-step explanation: I did ed ofcc

Caden owns 9 white t-shirts and 9 t-shirts in other colors ? If Caden randomly selects a t-shirt to wear, what is the probability it will be white?

Answers

Answer:

1/2

Step-by-step explanation:

Answer:

it is 1/2 or 9/18

Step-by-step explanation:

there was 18 shirts all together and half were white

good luck!

Help please and thank you

Help please and thank you

Answers

5/12 is what I got
Explanation:

Answer:

I checked it and the person above me is correct. Give em brainlyest! Your welcome other person

Step-by-step explanation:

the arizona department of transportation wishes to survey state residents to determine what proportion of the population would like to increase statewide highway speed to 75 from 65 mph. at least how many residents do they need to survey if they want to be at least 99% confident that the sample proportion is within 0.03 of the true proportion?

Answers

At least 99% confidence that the sample percentage is inside 0.03 of the absolute proportion is required for 1844 residents.

Choose p = 0.5 since the previous estimate of population percentage is uncertain.

E = 0.03 is the margin of error.

A 99% confidence interval requires the following crucial value: \(z_{a/2}\) = 2.576

The act of deciding how many observations or repetitions to incorporate into a statistical sample is known as sample size determination.

The sample size,

n = 0.5 × (1 - 0.5) × (\(z_{a/2}\) ÷ E)²

n = 0.25 × (2.576 ÷ 0.03)²

n = 1843.27 ≈ 1844

As a result, the needed sample size is 1844.

Read more about the sample proportion of confidence interval at

https://brainly.com/question/18485135?referrer=searchResults

#SPJ4

10x + 1 + 12x - 5 = 180 Find x

Answers

Answer:

x = 92/11

Step-by-step explanation:

10x + 1 + 12x - 5 = 180

*group the like terms*

(10x + 12x) + (1-5) = 180

*simplify*

22x - 4 = 180

*add four on both sides to cancel out -4*

+4. +4

*simplify*

22x = 184

*divide both sides by 22 to cancel out the quantity and solve for x*

÷22 ÷22

*simplify*

x = 92/11

Answer:

x = 92/11, x = 8.36 repeating the .36, or x = 8 4/11

Step-by-step explanation:

Angad was thinking of a number. Angad adds 11, then divides by 8 to get an answer of 5. What was the original number?

Answers

Answer:

29

Step-by-step explanation:

x+11÷8=5

5 × 8 = 40

40- 11 = 29

29 + 11 ÷ 8 =5

Given w= sqrt2 (cos ( pi / 4 ) + i sin ( pi / 4 ) ) and z = 2 (cos ( pi / 2 ) + I sin ( pi /2 ) ) , what is w – z expressed in polar form?

Answers

w = √2 (cos(π/4) + i sin(π/4)) = √2 (1/√2 + i/√2) = 1 + i

z = 2 (cos(π/2) + i sin(π/2)) = 2i

Then

w - z = (1 + i) - 2i = 1 - i

so that

|w - z| = √(1² + (-1)²) = √2

and

arg(w - z) = -π/4

In polar form, we have

w - z = √2 (cos(-π/4) + i sin(-π/4)) = √2 (cos(π/4) - i sin(π/4))

Answer:

Step-by-step explanation:

Given w= sqrt2 (cos ( pi / 4 ) + i sin ( pi / 4 ) ) and z = 2 (cos ( pi / 2 ) + I sin ( pi /2 ) ) , what

Determinar el valor de K,si:
K=(-1/2 + 7)¯² + 105⁰=

Answers

Answer:

\({ \tt{k = ( - \frac{1}{2} + 7) { }^{ - 2} + 105 {}^{0} }} \\ \\ { \tt{k = {( \frac{13}{2} )}^{ - 2} + 1 }} \\ \\ { \tt{k = {( \frac{2}{13}) }^{2} + 1}} \\ \\ { \tt{k = \frac{4}{169} + 1 }} \\ \\ { \tt{k = \frac{173}{169} }}\)

Which method do we not use when defining function?
A. Mapping method
B. Vertical line test
C. Horizontal line test
D. “Every x can only have one y”

Answers

I’ll say the answer is D I’m not sure tho !

helppppp meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

helppppp meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

Answers

Answer:

Step-by-step explanation:

helppppp meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

Answer:

a) 8:20

b) 14:28

Step-by-step explanation:

Solve the differential equation y'=1-y^2 Solve for y and explain your answer. Also state the equilibrium and nonequilibrium solutions.

Answers

y(x) = tan(x + C) where C is an arbitrary constant of integration. Thus, the equilibrium solutions are y = 1 and y = -1. The non-equilibrium solutions are the values of y that make y' not equal to 0.

EQUILIBRIUM AND NON-EQUILIBRIUM

The general solution to the differential equation y' = 1 - y² is:

y(x) = tan(x + C)

Where C is an arbitrary constant of integration.

The equilibrium solutions are the values of y that make y' = 0, which occur when y² = 1. Thus, the equilibrium solutions are y = 1 and y = -1.

The non-equilibrium solutions are the values of y that make y' not equal to 0. So the non-equilibrium solutions are the values of y that make y² different from 1, which are values of y that are not 1 or -1.

The solution y(x) = tan(x + C) is a family of functions indexed by the arbitrary constant C. The constant C cannot be determined from the information given in the problem, and so the general solution contains all possible specific solutions.

Learn more about the equilibrium and nonequilibrium here:

https://brainly.com/question/15231478

#SPJ4

10 points
Find the DISTANCE between point (3, -8) and point (-11,5). *

Answers

Answer:

19.1

Step-by-step explanation:

plsssssssssss help me

plsssssssssss help me

Answers

Answer: 40

Step-by-step explanation:

38+ 52=90

230-90=40

The division 4+2i/8-3i is performed by multiplying the numerator and denominator by

Answers

multiplying the numerator and denominator by (8+3i)

The division 4+2i/8-3i is performed by multiplying the numerator and denominator by (8+3i).

Given

The division 4+2i/8-3i is performed by multiplying the numerator and denominator by

Expression; \(\rm \dfrac{4+2i}{8-3i}\)

A complex conjugate is formed by changing the sign between two terms in a complex number i.e. a+ ib has conjugate a-ib and a- ib has conjugate like a+ ib.

The division 4+2i/8-3i is performed by multiplying the numerator and denominator by (8+3i).

\(=\rm \dfrac{4+2i}{8-3i}\\\\= \rm \dfrac{4+2i}{8-3i}\times \dfrac{8+3i}{8+3i}\\\\= \dfrac{(4+2i) \times (8+3i)}{(8)^2-(-3i)^2}\\\\= \dfrac{32+12i+16i+6i^2}{64+9}\\\\=\dfrac{32+28i+6i^2}{73}\)

Hence, The division 4+2i/8-3i is performed by multiplying the numerator and denominator by (8+3i).

To know more about Division click the link given below.

https://brainly.com/question/10628378

CAN YALL HELP ME WITH THIS ONEEE!!!!! PLZ

CAN YALL HELP ME WITH THIS ONEEE!!!!! PLZ

Answers

Answer:

b

Step-by-step explanation:

12x12

11x11

10x10

9x9

8x8

7x7

6x6

5x5

4x4

3x3

2x2

1x1

add em together equal 650

The answer is b I’ve already taking that question

Quick question: is this correct?

Quick question: is this correct?

Answers

Answer:

aha

you know what I mean

mean I guess your correct

Answer:

yes

Step-by-step explanation:

Can you help me match all of these :( please :(

Can you help me match all of these :( please :(

Answers

try looking the up

Step-by-step explanation:

trylooking them up

Which statement is sufficient evidence that DEF is congruent to ABC?

Which statement is sufficient evidence that DEF is congruent to ABC?

Answers

A or B? leaning more towards A tho

please please please help me

please please please help me

Answers

Answer:

360 cubic inches

Step-by-step explanation:

To find the volume of a rectangular, multiply its height by its width and by its length. We are given these values above.

8*5=40

40*9=360 cubic inches

Or:

8*5*9= 360 cubic inches

how do I solve this?

how do I solve this?

Answers

Answer: I cant see the problem

Step-by-step explanation:

Answer:

Where is the question?

Step-by-step explanation:

As the bus station, there are eight lines for arriving passengers, each staffed by a single worker. The arrival for passengers is 124 per hour and each passenger takes (on average) 3 minutes for a worker to process. The coefficient of variation for arrival time is 1,4 and the coefficient of variation for service time is 1.

How much time in minute will an how many customers spend in queue?

Answers

At the bus station, there are eight lines for arriving passengers, each staffed by a single worker. The arrival rate for passengers is 124 per hour, which means the arrival rate per minute is 124/60 = 2.067 passengers per minute. Each passenger takes an average of 3 minutes for a worker to process, so the service rate per worker is 1/3 = 0.333 customers per minute.

Since there are eight workers, the combined service rate for all workers is 8 * 0.333 = 2.664 customers per minute. The coefficient of variation for arrival time is 1.4, and the coefficient of variation for service time is 1.

To find the average number of customers in the queue, we can use the formula:

Lq = (Ca^2 + Cs^2) * (λ^2) / (2 * (µ - λ))

Where Lq is the average number of customers in the queue, Ca is the coefficient of variation for arrival time, Cs is the coefficient of variation for service time, λ is the arrival rate, and µ is the service rate.

Lq = (1.4^2 + 1^2) * (2.067^2) / (2 * (2.664 - 2.067))
Lq = (1.96 + 1) * (4.276) / (2 * 0.597)
Lq ≈ 7.34 customers in the queue

To find the average time a customer spends in the queue, we can use the formula:

Wq = Lq / λ

Wq = 7.34 / 2.067
Wq ≈ 3.55 minutes

On average, customers spend approximately 3.55 minutes in the queue.

To learn more about coefficients visit;

https://brainly.com/question/28975079

#SPJ11

Lina is making a spreadsheet for an assignment. The spreadsheet, when completed, will be 191 lines long, and Lina has already completed 59 lines.

x + 59 = 191

How many lines does Lina have left to complete?
A. 250
B. 221
C. 73
D. 132

Answers

The answer is D. 132. you subtract 59 from 191 and you get 132
It’s A I hope it was helpful

If the mean of a normal distribution is negative, Group of answer choices the variance must also be negative. none of these alternatives is correct. a mistake has been made in the computations, because the mean of a normal distribution cannot be negative. the standard deviation must also be negative.

Answers

The main answer to the question is: None of these alternatives is correct. If the mean of a normal distribution is negative, the variance must not be negative. The explanation to support the answer is given below:

Normal distribution is a statistical distribution that depicts how values are dispersed in a dataset. It is also known as Gaussian distribution or bell curve because of its bell-shaped pattern. It is described by two parameters, i.e., mean and standard deviation.The mean of a normal distribution specifies the location of the center of the distribution. The variance of a normal distribution indicates the amount of variation from the mean. Variance is always positive, no matter whether the mean is positive or negative.

Therefore, if the mean of a normal distribution is negative, the variance must not be negative.Hence, none of these alternatives is correct. If the mean of a normal distribution is negative, the variance must not be negative.

To know more about normal distribution visit:

https://brainly.com/question/15103234

#SPJ11

anyone HELP I WILL GIVE BRAINLIEST - its my sisters and i forgot everything in math shes in grade 9

anyone HELP I WILL GIVE BRAINLIEST - its my sisters and i forgot everything in math shes in grade 9

Answers

We have to find horizontal component of Mayosons velocity.

#a

\(\\ \tt\bull\leadsto V_x=vsin\theta\)

\(\\ \tt\bull\leadsto V_x=2.5sin36\)

\(\\ \tt\bull\leadsto V_x=2.5(0.58)\)

\(\\ \tt\bull\leadsto V_x=1.45m/s\)

#b

Here 2 vectors A=8 and B=2.5

\(\\ \tt\bull\leadsto \overrightarrow{R}\)

\(\\ \tt\bull\leadsto \sqrt{A^2+B^2+2ABcos\Theta}\)

\(\\ \tt\bull\leadsto \sqrt{8^2+2.5^2+2(8)(2.5)cos36}\)

\(\\ \tt\bull\leadsto \sqrt{64+6.25+40(0.8)}\)

\(\\ \tt\bull\leadsto \sqrt{70.25+32}\)

\(\\ \tt\bull\leadsto \sqrt{102.25}\)

\(\\ \tt\bull\leadsto 10.15m/s\)

HELP PLZ!! NOW!!!!! IM SLEEPY!!!!!!

HELP PLZ!! NOW!!!!! IM SLEEPY!!!!!!

Answers

Answer:

CHRISTMAS TREES

Step-by-step explanation:

for each number in the matrix, start by subtracting 1, then divide the number you got by 2

Jenna works a job where her pay varies directly with the number of hours she has worked. In one week, she worked 35 hours and made $274.75. How many hours would she need to work in order to earn $337.55?

Answers

274.75/35= $7.85 per hour
337.55/7.85= 43 hours

Figure J, the small quadrilateral, was dilated with the origin as the center of dilation to create Figure K, the large quadrilateral.

Which rule best represents the dilation that was applied to Figure J to create Figure K?

!you can open the image in a new tab to make it bigger!

Figure J, the small quadrilateral, was dilated with the origin as the center of dilation to create Figure

Answers

Answer:

(x, y) -> (2.5x, 2.5y)

Step-by-step explanation:

To find which equation is correct, first, let's find a similar point of Figure J and Figure K.

Figure J: (-3, -2). Figure K: (-7.5, -5)

As you can see, Figure J was enlarged by a SF of 2.5 because -3 x 2.5 = -7.5, and -2 x 2.5 = -5.

Therefore, the answer is (x, y) -> (2.5x, 2.5y).

hello please help thanks

hello please help thanks

Answers

Answer:

D

Step-by-step explanation:

it states that the snikholes are from underneath when the soil it lose

What is lim
x²-4?
X-2 X+2
O-4
O 0
04
ODNE

What is limx-4?X-2 X+2O-4O 004ODNE

Answers

Answer:

A

Step-by-step explanation:

\(\lim_{x \to -2} \frac{x^{2}-4 }{x+2} \\\lim_{x \to -2} \frac{(x+2)(x-2)}{x+2}\\ \lim_{x \to -2} x-2\\= -4\)

Answer:

First answer choice

\(- 4\)

Step-by-step explanation:

\(\lim _{x\to \:-2}\left(\dfrac{x^2-4}{x+2}\right)\\\\\\\mathrm{Simplify}\:\dfrac{x^2-4}{x+2}\\\\\\\mathrm{Factor}\:x^2-4:\quad (x + 2)(x - 2)\\\\\lim _{x\to \:-2}\left(\dfrac{x^2-4}{x+2}\right) \\\\= \lim _{x\to \:-2}\left(\dfrac{x+2)(x-2)}{x+2}\right)\)

The x+2 common factor cancels out

\(= \lim _{x\to \:-2}\left(x-2\right)\\\\\text{Plug in the value x= -2}\\\\= -2 - 2\\= -4\)

Other Questions
After flying from London to New York, Arthur experiences a restless, sleepless night. His problem was most likely caused by a disruption of his Select one: O A. sleep apnea. narcolepsy C. circadian rhythm. O D. hypnagogic sensations. anyoneeee knowww this is math i dont know what it is How would you obtain a mean value for the specific heatcapacity of a material? SHOW ALL YOUR WORK. REMEMBER THAT PROGRAM SEGMENTS ARE TO BE WRITTEN IN JAVA.Assume that the classes listed in the Java Quick Reference have been imported where appropriate.Unless otherwise noted in the question, assume that parameters in method calls are not null and that methods are called only when their preconditions are satisfied.In writing solutions for each question, you may use any of the accessible methods that are listed in classes defined in that question. Writing significant amounts of code that can be replaced by a call to one of these methods will not receive full credit.The following Pet class is used to represent pets and print information about each pet. Each Pet object has attributes for the pets name and species.public class Pet{private String name;private String species;public Pet(String n, String s){name = n;species = s;}public String getName(){return name;}public void printPetInfo(){System.out.print(name + " is a " + species);}}The following Dog class is a subclass of the Pet class that has one additional attribute: a String variable named breed that is used to represent the breed of the dog. The Dogclass also contains a printPetInfo method to print the name and breed of the dog.public class Dog extends Pet{private String breed;public Dog(String n, String b){super(n, "dog");breed = b;}public void printPetInfo(){/* to be implemented */}}Consider the following code segment.Dog fluffy = new Dog("Fluffy", "pomeranian");fluffy.printPetInfo();The code segment is intended to print the following output.Fluffy is a dog of breed pomeranian(a) Complete the Dog method printPetInfo below. Your implementation should conform to the example above.public void printPetInfo()Consider the following pets.A rabbit named FloppyA dog (whose breed is pug) named ArtyThe following code segment is intended to represent the two pets described above as objects pet1 and pet2, respectively, and add them to the ArrayList petList.ArrayList petList = new ArrayList();/* missing code */petList.add(pet1);petList.add(pet2);(b) Write a code segment that can be used to replace /* missing code */ so that pet1 and pet2 will be correctly created and added to petList. Assume that class Dog works as intended, regardless of what you wrote in part (a).The PetOwner class below is used to generate a description about a pet and its owner. The PetOwner constructor takes a Pet object and a String value (representing the name of the pets owner) as parameters.public class PetOwner{private Pet thePet;private String owner;public PetOwner(Pet p, String o){thePet = p;owner = o;}public void printOwnerInfo(){/* to be implemented */}}Assume that pet1 and pet2 were created as specified in part (b). The following table demonstrates the intended behavior of the PetOwner class using objects pet1 and pet2.Code SegmentResult PrintedPetOwner owner1 = new PetOwner(pet1, "Jerry");owner1.printOwnerInfo();Floppy is a rabbit owned by JerryPetOwner owner2 = new PetOwner(pet2, "Kris");owner2.printOwnerInfo();Arty is a dog of breed pug owned by Kris(c) Complete the PetOwner method printOwnerInfo below. Your implementation should conform to the examples. Assume that class Dog works as intended, regardless of what you wrote in part (a).public void printOwnerInfo() In the following graph we observe line segment AB being mapped by translation to line segment A'B'.A. In two or more sentences, explain what test you could perform to check the validity of this translation.B. Prove mathematically that the translation is valid using the test you mentioned above. solve em for me please Discrimination against or the putting down of groups of people on the basis of their social identity or characteristics is known as: What are the 3 key goals of the underwriting function?What are the 3 key goals of a claims adjuster when settling claims?What are 3 reasons that reinsurance is used? I'M GIVING BRAINIEST. why doesn't my mother love me. What is a marketpls tell a short ans Which security measure can be used to generate and store cryptographic keys?. Which pregnancy test is the best for early detection?. a) Beddington and May (1982) proposed the following model to study the interactions between baleen whales and their main food source, krill: Krill (x): dx dt =rX -axy dy Whales (v): = sy with r. K, a, s, b>0. dt Assume the units for time is years, for krill is 1,000,000,000's (billions), and for whales is 1,000's (thousands) for the ecosystem modeled by these equations. b) interpret what each term in the equation means (with its units), and nondimensionalize it. nflation can impose significant costs and adversely distort economic systems. indicate whether the costs and distorting effects exemplify menu costs, shoe leather costs or unit of account costs. a. discourages people from holding money b. can reduce the quality of economic decisions menu costs c. can lead to stores listing prices in more stable currencies d. spending time converting money into something that better holds value e. makes money a less reliable source of measurement f. can cause distortion to the tax system g. causes difficulty in firms and individuals financial planning h. causes costs associated with changing prices in stores NEED discussionIs it possible for an economy to be based entirely on services?FULLY ANSWER PLEASETHANK YOU. If you want to buy a car in NY that costs $8,200 and requires a down payment of 10%, what is the amount of the down payment? (Hint: NY sales tax is 8.6% Mrs. Allen made 8 pitchers of fruit punch for a party. She used 2 liters of waterto make each pitcher of fruit punch. How many liters of water did Mrs. Allenuse in all? Charlotte is driving at 52.7 mi/h and receives a text message. She looks down at her phone and takes her eyes off the road for 4.99 s. How far has Charlotte traveled in feet during this time Exercise 1 Add commas where necessary. Delete commas used incorrectly using the delete symbol .We also saw the Museum of Modern Art my favorite spot of all. If the fixed costs of manufacturing a new jet ski are $27,000, the sales price is $10,000, and the variable cost per unit is $1,000, the break-even point is.