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
iogann1982 [59]
3 years ago
13

Breaking stuff let {xi} n i=1 be a sample of random variables of size n with the property that xi ∼ n (µ, σ2 ) and cov(xi , xj )

= ρσ for all pairs i, j.
a.solve for the mean and variance of x¯.
b.what happens to the variance of x¯ as n → ∞?
c.why do the clt and lln fail in this situation?
d.using the provided code, simulate s = 1000 values of x¯ for n = 50, 100, 500. in all three cases calculate the mean and variance of the resulting distribution. create histograms for each. in this code, σ = 1 and ρ = .4. how does the variance for each n compare to the formula from part (a)?
Mathematics
1 answer:
hammer [34]3 years ago
4 0

With

\bar X=\displaystyle\sum_{i=1}^n\frac{X_i}n

we find the mean is

\mathrm E[\bar X]=\displaystyle\frac1n\sum_{i=1}^n\mathrm E[X_i]=\frac{n\mu}n=\mu

and the variance is

\mathrm V[\bar X]=\displaystyle\frac1{n^2}\mathrm V\left[\sum_{i=1}^nX_i\right]

\mathrm V[\bar X]=\displaystyle\frac1{n^2}\left(\sum_{i=1}^n\mathrm V[X_i]+2\sum_{1\le i

\mathrm V[\bar X]=\displaystyle\frac1{n^2}\left(n\sigma^2+2\frac{n(n-1)}2\rho\sigma\right)

\mathrm V[\bar X]=\dfrac{\sigma^2}n+\dfrac{n-1}n\rho\sigma

Then as n\to\infty, we find that \mathrm V[\bar X]\to\rho\sigma. Simply put, the failure of the CLT/LLN has to do with the fact that the X_i are not independent.

You might be interested in
Vertical, Complementary and Linear Pair Angles help me please
Mariana [72]
I saw this same type of question and page but with different numbers just 5 minutes ago...

Anyway here’s the answers:
1) Complementary
3x+1+44=90
3x+45=90
3x=45
x=5
2) Vertical
Ignore everything about the work. The answer is 120 degrees because they’re vertical angles.
3) Supplementary
15x-5+110=180
15x+105=180
15x=75
x=5
And I can’t see the last question clearly
5 0
3 years ago
PLEASE HELP 15 POINTS...PLEASE HELP
sasho [114]

Answer:

-4

Step-by-step explanation: it is intercepting the -4 so i think -4 is the right answer

8 0
3 years ago
Read 2 more answers
If my heart beats 2790 times every three quarters of an hour, what is your heart rate per minute?
kodGreya [7K]

Your heart rate is the number of times each minute that your heart beats, which is normally between 60 and 100 times per minute for adults. Your pulse is a way you can feel each time your heart beats. Measuring your heart rate helps you monitor your own health and know if you’re exercising at the right level to get the most benefits to your health.

Your pulse is your heart rate, or the number of times your heart beats in one minute. Pulse rates vary from person to person. Your pulse is lower when you are at rest and increases when you exercise (more oxygen-rich blood is needed by the body when you exercise). Knowing how to take your pulse can help you evaluate your exercise program.

5 0
2 years ago
Read 2 more answers
Write the contrapositive of the conditional statement. Determine whether the contrapositive is true or false. If it is false, fi
Mila [183]
If you are 16 years old then you are a teenager Question 14
6 0
3 years ago
Find the equation of the plane z = mx + ny + b which contains the points (0,0,6), (1,0,-3) and (0,2,5).
leonid [27]
The three points give you three equations, which you can solve by your favorite method.
.. 0m +0n +b = 6
.. 1m +0n +b = -3
.. 0m +2n +b = 5

(m, n, b) = (-9, -1/2, 6)
so the equation of the plane can be written as
.. z = -9x -1/2y +6

_____
In standard form, this would be
.. 18x +y +2z = 12

8 0
3 years ago
Other questions:
  • Write the equation of the line passing through the given point with the indicated slope.
    13·1 answer
  • Use what you have learned about filing income taxes to complete these sentences.
    12·2 answers
  • What is the length of segment IO? (io) <br> G H I J K L M N O<br> -7-6-5-4-3-2-1 0 1
    15·1 answer
  • a Christian University found that about 3% of its students came from certain state the university had 156 students from that sta
    11·1 answer
  • Write an equation for each transformation of y = x
    12·1 answer
  • Brett has 2 1/2 pounds of bird seed left to share equally among 4 bird cages in his pet shop. How many pounds can he put in each
    8·1 answer
  • What is the volume of a cone if the diameter is 8 and the height is 12
    14·1 answer
  • Pls help me with this
    10·1 answer
  • Write the expression in its simplest form : -3 (7h+1)+6h
    13·2 answers
  • You are planning your week-end schedule. You can spend at most 8 hours playing video games and doing homework. You want to spend
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!