Let 1, 2, · · · be i.i.d. r.v.s with mean 0, and let = 1 + · · · + .
a) Find(1 |).
b) Find ( | ) for 1 ≤ ≤ .
c) Find ( | ) for > .

Answers

Answer 1

When 1, 2, · · · is i.i.d. r.v.s with mean 0, and = 1 + · · · +

a) for (1 |) will be 0.

b) for ( | ) for 1 ≤ ≤  is the reciprocal of the number of variables.

c) for( | ) for > . is simply 1.

What is the conditional expectations for a sequence of i.i.d. random variables?

(a) To find [tex]E(1 | )[/tex], we can use the formula for conditional expectation:

[tex]E(1 | ) = E(1) + Cov(1, ) / Var()[/tex]

Since the random variables are i.i.d., we know that Cov(1, ) = 0 and Var() = Var(1) + Var(2) + ... + Var(). Since each variable has mean 0, we have Var(1) = Var(2) = ... = Var(). Let's call this common variance σ^2. Then we have:

[tex]E(1 | ) = E(1) = 0[/tex]

So the conditional expectation of the first random variable, given the sum of all the variables, is simply 0.

(b) To find [tex]E(i | )[/tex], where 1 ≤ i ≤ , we can use a similar formula:

[tex]E(i | ) = E(i) + Cov(i, ) / Var()[/tex]

Since the variables are i.i.d., we have [tex]Cov(i, ) = 0 for i ≠ j[/tex]. So we only need to consider the case where i = j:

[tex]E(i | ) = E(i) + Cov(i, ) / Var()[/tex]

[tex]= 0 + Cov(i, i) / Var()[/tex]

[tex]= Var(i) / Var()[/tex]

[tex]= 1/[/tex]

So the conditional expectation of any individual variable, given the sum of all the variables, is simply the reciprocal of the number of variables.

(c) Finally, to find[tex]E( | )[/tex], where > , we can again use the same formula:

[tex]E( | ) = E() + Cov(, ) / Var()[/tex]

Since > , we know that [tex]Cov(, ) = Var()[/tex]. Also, we know that [tex]E() = 0[/tex] and [tex]Var() = σ^2[/tex]. Then we have:

[tex]E( | ) = E() + Cov(, ) / Var()[/tex]

[tex]= 0 + Var() / Var()[/tex]

[tex]= 1[/tex]

So the conditional expectation of the sum of all the variables, given that the sum is greater than a particular value, is simply 1.

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Related Questions

can somebody please help me with this I’m currently failing this class .. I’ll really appreciate it

Answers

umm so

Step-by-step explanation:

wait ill answer that just now let me work it out

i need help with these two due today plssss help me

Answers

Answer:

10. 264

11. 13

Step-by-step explanation:

10- When we are doing perimeter we add all the sides together. Since it's a square this time, we know all the sides are even at 66ft.

 66+66+66+66= 264

 I added 4 times for each side we have and we get the perimeter of 264

11- When dealing with area, all we need is two numbers. To get area we multiply the length and width. If we have the area and want either length or width, we can still easily do that. All we have to do is divide the area from your given number.

 65 divided by 5 is 13

 Area divided by Length is Width

Answer:

#10= 264

#11= 13

Step-by-step explanation:

#10: We can see that this is a square because it says so in the question so we can assume that if it is a square then all the lengths and widths are 66 feet. 4(66) = 264 or 66+66+66+66 = 264

#11: 65/5 = 13 because it is dealing with area, simply just divide the total of area by the known length to get the width.

A company has recently been hiring new employees. Today the company has 35% more employees than it did a year ago. If there are currently
43,200 employees, how many employees did the company have a year ago?

Answers

Answer:

28,080

Step-by-step explanation:

Turn 35% into a decimal (.35)Multiply .35 by the amount of current employees (.35 * 43200 = 15120)Subtract the current amount of employees (43200) by 15120 (the amount of employees that joined) which should be 28080. This is your answer.


What is the GCF of 45x^5
and
36x^9

Answers

Answer:

9x^5

Step-by-step explanation:

the factors of 45:

1, 3, 5, 9, 15, 45

the factors of 36:

1, 2, 3, 4, 6, 9, 12, 18, 36

Greatest common is 9

Answer:

The answer is 3

Step-by-step explanation:

because I said so

Find the GCF: 12,24,36​

Answers

Answer:

12 is the GCF..........

Answer:

12

Step-by-step explanation:

listing the factors

12 : 1, 2, 3, 4, 6, 12

24 : 1, 2, 3, 4, 6, 8, 12, 24

36 : 1, 2, 3, 4, 6, 9, 12, 18, 36

The common factors are 1, 2, 3, 4, 6, 12

The GCF is 12

2x-7=8. find the value of x​

Answers

The answer is X=15/2
Move all terms that don't contain
x to the right side and solve.
So you would first Add 7 to both sides. 2x=8+7
Then simply 8+7 to 15 so 2x=15
Then Divide both sides by 2
To get x=15/2
Hope that helps

Which graph represents an exponential function?

Answers

The second graph represents the exponential function

Answer:

second which would be c for edg

Step-by-step explanation:

There are 9 gallons of paint for the students to use to paint the fence outside of the schoolyard. Each student has a bucket that holds 1/3 gallon. How many buckets does the 9 gallons of paint fill?

Answers

Answer:

27 buckets.

Step-by-step explanation:

If we multiply the 9 gallons of paint by the denominator of the number of gallons that fit into one of the buckets we can discover the answer to the question.

Brainliest please.

PLEASE HELP IT WOULD BE VERY MUCH APPRECIATED! Last year, James earned £1,600 per month.
This year, he's had a 2% increase in his monthly pay.
He worked 35 hours per week for 46 weeks in the year.
What is James' average pay per hour this year?
Give your answer to 2 dp.

Answers

Answer: £11.69

Explanation:

1) Work out 2% of £1600:
1600 x 2/100 =36

2) Add it on to the original number to get his new monthly pay:
1600 + 36 = £1636

3) Work out his yearly pay by:

a) finding the amount of months he worked:
46 / 4 = 11.5 months

b) Divide 11.5 into 2 bits and add them on:
1636 x 11 = 17997
1636 x 0.5 = 818

17997 + 818 = £18814

4) To get his pay per week:

18814 / 46 = £409

5) Finally, to get his pay per hour:

409 / 35 = 11.68671...
= £ 11.69

Answer:

Your answer is

12$ per hour

Want more answer then follow me, like and MARK MY ANSWER AS BRAINLIST ANSWER.

I need that urgently.

how many minutes would it take rachel to jog 3 miles if she jogs 1/15 mile every minute

Answers

Answer:

3 mi * 15 min/mi = 45 min

Step-by-step explanation:

the difference of 10 and a number is -2 what is the answer ​

Answers

Answer:

The answer is 8.

Step-by-step explanation:

This question can be written as the equation x-10=-2. With this equation in mind we can get straight ahead to solving. This is just a one-step equation and all we need to do to get our answer from this point is just add 10 to both sides using the addition property of equality and once we do that we have X=8.

Help please please please! WILL MARK BRAINLIST

Answers

Answer: I think it is A or B

Step-by-step explanation:

Please help ❤️❤️❤️❤️❤️❤️

Answers

Answer:

[tex]\frac{-1}{7}[/tex] or 0.14

Step-by-step explanation:

To find slope you can use the formula

mx=[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

or

[tex]\frac{rise}{run}[/tex]

Rise over run:

Rise over run is the easiest of the two so we'll be using that one first for this question, but both should give you the same answer

To find rise over run, select the points and see how many points up or down you must got to make it the same level as the other point

In this case, the point (-3,1) would have a run of -1 because you have to move down one

To find run, now that you have rise start from that point and count how far you have to go to get to the next point. You should be going in a straight line.

The run would be 7.

Now you make it a fraction/division problem

[tex]\frac{rise}{run} =\frac{-1}{7}[/tex]

-0.14285714285714285714285714285714 <- decimal value

-0.14

Depending on what it means by reduce, your answer will either be -1/7 or the decimal. Use the reduced decimal value if it's asking for a decimal

I've included a picture in case my explanation was not satisfactory or you need a visual.

Slope form:

Identify the two points

First one will be (-3,1)

Second one would be (4,0)

Now label them

-3 will be x1

1 is y1

4 is x2

0 is y2

You will be using [tex]\frac{y2-y1}{x2-x1}[/tex]

Put the values into the equation

[tex]\frac{0-1}{4--3} =\frac{0-1}{4+3} =\frac{-1}{7}[/tex]

You get the same thing as the previous way.

Same answer

Visuals also included

I hope this helps and don't be afraid to reach out with further questions!

A shop makes £2,750 in March. It has an Easter sale and the profit for April is £3,162.50 Work out the percentage increase

Answers

Answer: 15%

Step-by-step explanation:

From the question, we are informed that a shop makes £2,750 in March while it made £3,162.50 in April. The increase will be:

= £3,162.50 - £2,750

= £412.50

Percentage increase = £412.50/ £2750 × 100

= 15%

A sandwich store charges $20 to have 3 turkey subs delivered and $26 to have 4 delivered. How much does the store charge for the one additional turkey sub?

Answers

Answer:

Seven dollars

Step-by-step explanation:

show that the ratios 14/18 and 28/36 form a proportion by finding a common multiplier.

Answers

Step-by-step explanation:

divide it by 2...............

86, 82, 78, 74 , what is the 40th sequence

Answers

Answer:

The numbers slowly decrease by 4 so we can determine that the 40th sequence is -70.

Step-by-step explanation:

Do 4x and 15 + x have the same value when x is 5? How do you know?

Answers

Answer:

yes

Step-by-step explanation:

If x = 5,

4x=4*5=20

15+x=15+5=20

They're both the same.

Yes

Step-by-step explanation:

x = 5

4(5) = 15 + (5)

20 = 20

Which of the following values is the solution to the equation
-16 + x = -30 ?

-2
-14
-46
-480

Answers

Answer:

-14

Step-by-step explanation:

so we see -30-(-16)=-30+16=(-14)

hope it helps you

please mark me as brainlist

[tex]18 = -5b - 17[/tex]

Answers

Answer:

b = -7

Step-by-step explanation:

18 = -5b-17

Add 17 to each side

18+17 = -5b-17+17

35 = -5b

Divide each side by -5

35/-5 = -5b/-5

-7 = b

Which additional piece of information would allow you to
prove that the triangles are congruent by the HL theorem?

Answers

Answer:

D - Line AC is congruent to line DF

Explanation:

Options A and B are definitely incorrect. And while lines AB and DE seem congruent, there is no congruency line in between to confirm that. So option C is incorrect.
As for option D, there is a congruency line in between that confirms they are both congruent.

Hope it helps. ^^

The additional piece of information would allow you to prove that the triangles are congruent by the HL theorem is AB ≅ DE

What is HL theorem?

The HL Postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.

Given that two triangles Δ ABC and Δ DEF,

To prove them congruent by HL Postulate, we need one more side to be congruent, as the hypotenuse of both are already congruent.

Therefore, the sides should be either BC ≅ FE or AB ≅ DE

In options, AB ≅ DE is given.

Hence, The additional piece of information would allow you to prove that the triangles are congruent by the HL theorem is AB ≅ DE

For more references on HL theorem, click;

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find the product of (2x^2+2x-3)(4x^2-3x+6

Answers

Answer:

=8x^4+2x^3−6x^2+21x−18

Step-by-step explanation:

(2x2+2x−3)(4x2−3x+6)

Identify the independent and dependent variables in the equation y = 3x + 5
Group of answer choices

y is independent and x is dependent

x is independent and y is dependent

both x and y are independent

both x and y are dependent

Answers

Answer:

A system of equations consists of two or more equations with two or more variables, where any solution must satisfy all of the equations in the system at the same time.

PLEASE HELP ITS DUE SOONNNNN

Answers

Answer:

1 is correct.

2 is incorrect.

3 is correct.

4 is correct.

5 is correct.

6 is incorrect.

Step-by-step explanation:

You're welcome, hope I helped.

oouuu i’m glad the person above helped

In slope-intercept form ?

Answers

Jdjdjdjdmdjodkekeodkkd

Answer:

A) $5.5= 0.25(17)+0.05(n) where n = nickels

B) 25 nickels

Step-by-step explanation:

A circle has a circumference of 1{,}133.541,133.541, comma, 133, point, 54 units.
What is the diameter of the circle?


units

Answers

Answer:

can u give me the formula for this then i might be able to help

Step-by-step explanation:

Answer:

360.81

Step-by-step explanation:

What is 3/8 simplified and divided please show steps

Answers

Answer:

0.375

cannot be simplified more.

Step-by-step explanation:

three is prime, meaning it can only be divided by 1 and itself. When you see a prime in a fraction, you cannot simplify anymore without accidentally making it more complicated. Divided would just be the decimal form. The decimal form of 1/8 is 0.125, so if you multiply it by three you should get 3/8=0.375

4. Sarah, Toby, and their mother run an online store called Unique Bracelets that sells handmade bracelets consisting of unique, individually-painted charms. Each bracelet they sell consists of 12 small charms and 5 large charms. Each order also gets 5 blank spacer charms to use to separate charms or fill in the bracelet. They do not sell charms separately and do not sell bracelets in parts. (f) Write an equation showing the number of charms, y, needed for x bracelets purchased in an order. Describe what the equation means in a real-world context.

Answers

Complete question :

Sarah, Toby, and their mother run an online store called Unique Bracelets that sells handmade bracelets consisting of unique, individually painted charms. Each bracelet they sell consists of 12 small charms and 5 large charms. Each order also gets 5 blank spacer charms to use to separate charms or fill in the bracelet. They do not sell charms separately and do not sell bracelets in parts.

(a) Write an equation showing the number of charms, y, needed for x bracelets purchased in an order. Describe what the equation means in a real-world context.

(b) Sarah’s and Toby’s mother says the order she is filling needs 158 charms. How many bracelets were purchased in this order?

(c) Toby says they don’t have enough charms to fill an order that needs 264 charms. Sarah says it’s notpossible for an order to need 264 charms. Is Sarah right? Why or why not? Justify your answer.

Answer:

y = 17x + 5 ;

9 bracelets ;

Sarah is right

Step-by-step explanation:

Contents per bracelet :

Small charms per bracelet = 12

Large charms per bracelet = 5

Blank spacer charms per order = 5

Number charms, y needed for X bracelets in an order ;

1 order ; x bracelets

12 + 5 = 17 small and large charms

5 = black spacer charms per order

y = 17x + 5

B.)

Order requiring 158 charms, number of bracelets :

y = 158

158 = 17x + 5

158 - 5 = 17x

153 = 17x

x = 153 / 17

x = 9 bracelets

Order requiring 264 charms

y = 264

264 = 17x + 5

264 - 5 = 17x

259 = 17x

x = 259 / 17

x = 15.23 bracelets

Sarah is right, the number of bracelets should be a positive integer and not a decimal.

please help me what is the answers

Answers

Answer:

What is your question. Please refer to a single question.

Do the ratios 4/12 and 10/30 form a proportion? yes or no

Answers

Answer:

Yes because you can multiply the numerator and denominator by 2.5 to get 10/30 so it is proportional

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

it makes 2/3 when reduced

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