ρh=1 for h=0, for the auto-correlation function is given by the function: ρh={1 if h=0 0 if h≠0
Given that Xt=εt+0εt−2 and
{ε}~ WN(0,1).
We need to calculate the auto-covariance and auto-correlation functions of the given process (time-series).
a) Calculation of auto-covariance function:
Auto-covariance function is given by:
Cov(Xt, Xt+h)=Cov(εt, εt+h)+0Cov(εt, εt+h-2)+0Cov(εt-2, εt+h)+0Cov(εt-2, εt+h-2)
From the given process,
Cov(εt, εt+h)=0 when h≠0.
Hence, Cov(Xt, Xt+h)=0+bCov(εt-2, εt+h) for h > 0
Cov(Xt, Xt+h)=0+bCov(εt, εt+h-2) for h < 0
Cov(Xt, Xt+h)=0+b2 for h = 0
From White-noise (WN) process,
Cov(εt, εt+h)=0 when h≠0
and
Cov(εt, εt)=Var(εt)
=1
Then, Cov(εt, εt+h-2)=0 when h≠2 and
Cov(εt, εt-2)=Var(εt-2)
=1
Hence, Cov(Xt, Xt+h)=0+b ;if h=2
Cov(Xt, Xt+h)=0+b ;if h=-2
Cov(Xt, Xt+h)=b2 ;if h=0
Therefore, the auto-covariance function is given by
;Cov(Xt, Xt+h)={b if h=2 or h=-2 b2 if h=0b)
Calculation of auto-correlation function:
Auto-correlation function (ACF) is defined as follows;
ρh=Cov(Xt, Xt+h)/Cov(Xt, Xt)
From part (a), we know that
Cov(Xt, Xt+h) for h≠0 is zero.
Thus, ρh=0 for h≠0.
When h=0, Cov(Xt, Xt+h)=Var(Xt) which is equal to 1,
since εt~WN(0,1).
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For many relatively simple probability questions such as these, you should find that the math and calculations involved are not at all onerous. The trick is recognizing which concepts apply, and therefore which tools (e.g. formulas) are most appropriate for the job. It is equally important to recognize when the tools in your toolbox do NOT apply! This is so that when looking at data in the real world, or if you are looking at someone else's interpretation of data, you recognize when people are not using or interpreting the data appropriately.
For any confidence interval questions, you should provide a properly formatted confidence interval statement as your answer.
In solving simple probability questions, the calculations involved are usually straightforward. The key lies in identifying the applicable concepts and selecting the appropriate tools or formulas. Equally important is recognizing when these tools do not apply, enabling proper interpretation of data.
Understand the problem: Carefully read and comprehend the question to determine what information is given and what needs to be calculated. Identify the relevant concepts and tools that can be utilized.
Select the appropriate formula: Based on the problem statement and the involved concepts, choose the relevant formula or method to calculate the probability or confidence interval. Examples include the addition rule, multiplication rule, or Bayes' theorem.
Apply the given information: Substitute the known values into the formula, ensuring proper assignment and consistency of units.
Perform the calculations: Use mathematical operations to compute the desired probability or confidence interval. Take note of any special conditions or considerations mentioned in the problem.
Provide a clear answer: Express the result in a well-formatted manner. For probability questions, the answer may be a single value or a range, depending on the problem. Confidence interval questions require a properly formatted statement that includes the estimated parameter, range, and confidence level.
Validate and interpret the answer: Review the calculations for accuracy, and round the answer if necessary. Additionally, interpret the result within the context of the problem, providing explanations or conclusions as needed.
By practising with a variety of probability problems and confidence interval questions, you can improve your ability to identify relevant concepts and select the appropriate tools to solve them accurately. Furthermore, this practice will enhance your skills in recognizing when others may be misusing or misinterpreting data in real-world scenarios.
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What is the factored form of 6x²+13x+5?
Answer:
x1=-1/3 and x2=-1/5
3(3x+1)+2(5x+1)
3x+1=0,5x+1=0
×=-1/4 x=-1/5
give a database of the results of an election, find the number of seats won by each party
To find the number of seats won by each party from a database of election results, we need the specific information about the parties, the candidates, and the corresponding vote counts or seat allocations.
With that information, we can perform calculations or queries to determine the number of seats won by each party.
Here's a general outline of the steps involved:
Obtain the election database or data that includes information on parties, candidates, and their respective vote counts or seat allocations.
Analyze the database structure to identify the relevant tables or fields
that store the necessary information.
Use database query or analysis tools to extract the relevant data. Write a query or use filtering mechanisms to retrieve the party names, candidate information, and corresponding vote counts or seat allocations.
Perform calculations or aggregations based on the data retrieved to determine the total number of seats won by each party. This can involve summing the vote counts or seat allocations for each party.
Present or display the results, showing the number of seats won by each party in the election.
Please provide the specific database structure or information about the parties, candidates, and vote counts if you have them, and I can assist you further in generating the desired results.
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Combine the like terms to create an equivalent expression for −4y−4+(−3)
Answer:
-4y - 7
Step-by-step explanation:
−4y−4+(−3)
-4y - 4 - 3
-4y - 7
please help.
I need which letters to click
Translate the phrase into an inequality:
Seven plus a number x is at most twenty
At most means less than or equal to:
7 + x ≤ 20
PLEASEEEEE HELP ME ON THIS
may not know the answer that well but try this called symbolab. Hope that could help you
-1.2k + 3.9 - g + .5g + 7 + .3k
Answer:
hi
Step-by-step explanation:
Given that sin(u) = 5/13 for 0 <= u <= π and tan(v)= -3/4 for π/2 <= v <= π. Find the values of Sin (u+v).
The value of sin(u+v) is -16/13. The value of sin(u+v) can be determined using trigonometric identities and the given information. We are given that sin(u) = 5/13 for 0 ≤ u ≤ π and tan(v) = -3/4 for π/2 ≤ v ≤ π.
To find sin(u+v), we need to use the sum of angles formula for sine. According to this formula, sin(u+v) = sin(u)cos(v) + cos(u)sin(v).
From the given information, we know the value of sin(u) = 5/13. To find cos(u), we can use the Pythagorean identity [tex]sin^2(u) + cos^2(u) = 1[/tex]. Plugging in the value of sin(u), we have [tex](5/13)^2 + cos^2(u) = 1[/tex]. Solving for cos(u), we find cos(u) = 12/13.
Similarly, we know that tan(v) = -3/4. Using the identity tan(v) = sin(v)/cos(v), we can solve for sin(v) and cos(v). We have sin(v)/cos(v) = -3/4, which implies sin(v) = -3 and cos(v) = 4.
Now we have all the values needed to calculate sin(u+v). Substituting the known values into the sum of angles formula, we get sin(u+v) = (5/13)(4) + (12/13)(-3) = 20/13 - 36/13 = -16/13.
Therefore, the value of sin(u+v) is -16/13.
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Lollipops cost 12p each, but I get 3 for 30p. What is the maximum number of lollipops I can buy if I have £2 to spend?
Answer:
18 lolly pops
Step-by-step explanation:
3 = 30p
3x6 = 1.80
= 18
Solve the differential equation (D2 + 4)y=6 sin2x +3x2 =
The general solution to the differential equation (D^2 + 4)y = 6sin(2x) + 3x^2 is y = A sin(2x) + B cos(2x) + (3/4)x^2.
To solve the given differential equation (D^2 + 4)y = 6sin(2x) + 3x^2, where D represents the derivative operator, we can use the method of undetermined coefficients.
The homogeneous solution to the equation is y_h = A sin(2x) + B cos(2x), where A and B are arbitrary constants.
To find the particular solution, we assume y_p = Cx^2 + Dx + E as it contains the same form as the non-homogeneous term. By substituting y_p into the equation and comparing coefficients, we find that C = 3/4.Therefore, the general solution to the differential equation is y = A sin(2x) + B cos(2x) + (3/4)x^2, where A and B are arbitrary constants. This solution accounts for both homogeneous and particular solutions.
The specific values of A and B can be determined by applying initial or boundary conditions if given.
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Ethan makes punch by mixing orange juice with
sparkling water. He uses the same ratio of orange juice
to sparkling water each time he makes punch. The table
shows some of the amounts of orange juice and
sparkling water he uses for different amounts of punch.
Orange Juice (fl oz) 7 21 28 ?
Sparkling Water (fl oz) 4 12 16 28
If Ethan uses 28 fl oz of sparkling water, how much orange juice will he use and what will be the total amount of punch?
Use the number pad to enter your answers in the boxes.
Ethan will use ____
fl oz of orange juice, and he will have a total of ___
fl oz of punch.
Answer:
Ethan will use 49
fl oz of orange juice, and he will have a total of 77
fl oz of punch.
Step-by-step explanation:
He uses a ratio of 7 to 4 of orange juice to sparkling water.
7/4 = ?/28
4 * ? = 7 * 28
Divide both sides by 4.
? = 7 * 7
? = 49
He will use 49 fl oz of orange juice.
The total amount made is: 49 fl oz + 28 fl oz = 77 fl oz
Answer:
Ethan will use 49
fl oz of orange juice, and he will have a total of 77
fl oz of punch.
Estimate the area of tje fan if m
Answer:
Area of the given fan is 763.4 cm²
Step-by-step explanation:
Area of a sector in a circle = [tex]\frac{\theta}{360}(\pi r^2)[/tex]
Here, angle θ = Central angle subtended by the arc
r = Radius of the circle
Since, fan is in the form of a sector of a circle with radius = 27 cm
Measure of the central angle subtended by the arc FN = ∠FAN = 120°
Area of the fan = [tex]\frac{120}{360}(\pi )(27)^2[/tex]
= [tex]\frac{729\pi }{3}[/tex]
= 243π
= 763.407
≈ 763.4 cm²
Therefore, area of the given fan is 763.4 cm²
Please helppp I need this for a better grade
Answer:
Step-by-step explanation:
Cos(x)=18/44=0.41
x=65.85
The distance between two cities on a map measure 3.71 inches. The scale on the map shows that 2 inches is equal to 50 miles. How many miles apart are the two cities
Answer:
92.75 miles
Step-by-step explanation:
3.71 / 2 = 1.855
1.855 * 50 miles = 92.75 miles
If shooting in different light sources each light source should have a different custom color profile. True False
The statement "If shooting in different light sources each light source should have a different custom color profile" is False.
Shooting in different light sources does not necessarily require different custom color profiles. The purpose of a color profile is to ensure accurate color reproduction across different devices and environments. While different light sources may have different color temperatures and characteristics, modern cameras and editing software often provide options to adjust white balance and color settings to account for different lighting conditions.
These adjustments can help achieve consistent and accurate colors without the need for separate custom color profiles for each light source. However, in certain professional or specialized applications, such as high-end photography or color-critical work, custom color profiles may be created to fine-tune color accuracy based on specific lighting conditions.
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Choose the function whose graph is given by:
O A. y=tan(x + 2) - pi
O B. y=tan(x - pi) + 2
O C. y=tan(x-pi) - 2
D. y=tan(2(x + pi)) + 2
it’s b!!!
Answer:
d
Step-by-step explanation:
y=tan (2(x+2)-2, I think that is it
Answer:
y=tan(x-pi)-2
Step-by-step explanation:
How would you use the unit rate to find the number of cups of dry rice you would need to serve 50 people?
the unit rate is 3 people/1 cup of rice.
Answer:
3 people/1 cup
50/3 = 16.68 cups of dry rice
May someone please help me with this :)
Answer:
3,080 cm
Step-by-step explanation:
simple -. -
can someone dooo ittttttttt
Answer:
i dont know
Step-by-step explanation:
Which of the below is an advantage of nonparametric statistical procedures? There is more than one possibility.
Choose one answer.
a. They require a large sample size
b. The results are less powerful
c. Fewer requirements need to be met
d. The computations are easy
The advantage of nonparametric statistical procedures is that they require fewer requirements to be met. This means that nonparametric statistical procedures are more flexible than parametric ones.
Statistical procedures refer to a collection of mathematical techniques that allow researchers to conduct statistical analyses. Statistical procedures are usually classified as either parametric or nonparametric.
A statistical procedure is considered parametric if it assumes that the population follows a specific distribution.
A statistical procedure is considered nonparametric if it does not assume that the population follows a particular distribution.
One of the advantages of nonparametric statistical procedures is that they require fewer assumptions than parametric statistical procedures. This means that they are more flexible and can be used in situations where the assumptions of parametric statistical procedures are not met.
Additionally, nonparametric statistical procedures are more robust to outliers and can be used when the data are skewed or have a non-normal distribution.
Another advantage of nonparametric statistical procedures is that they are easy to compute.
Unlike parametric statistical procedures, which require complex computations, nonparametric statistical procedures can be calculated using simple methods that are easy to understand.
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As an avid cookies fan, you strive to only buy cookie brands that have a high number of chocolate chips in each cookie. Your minimum standard is to have cookies with more than 10 chocolate chips per cookie. After stocking up on cookies for the current Covid-related self-isolation, you want to test if a new brand of cookies holds up to this challenge. You take a sample of 15 cookies to test the claim that each cookie contains more than 10 chocolate chips. The average number of chocolate chips per cookie in the sample was 11.16 with a sample standard deviation of 1.04. You assume the distribution of the population is not highly skewed. Alternatively, you're interested in the actual p value for the hypothesis test. Using the previously calculated test statistic, what can you say about the range of the p value?
The test statistic is 1.09. The p-value is the probability of obtaining a test statistic at least as extreme as the one observed, assuming the null hypothesis is true. The range of the p-value is 0.1 to 1.
How to explain the informationIf the p-value is less than 0.05, we reject the null hypothesis and conclude that the new brand of cookies has more than 10 chocolate chips per cookie.
If the p-value is greater than 0.05, we fail to reject the null hypothesis and cannot conclude that the new brand of cookies has more than 10 chocolate chips per cookie.
In this case, the p-value is between 0.1 and 1. Therefore, we cannot conclude that the new brand of cookies has more than 10 chocolate chips per cookie.
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To solve for x in the equation x + 3 = 5, you would...
answer/ step-by-step explanation:
hi there!
the question is asking us to solve for x for the equation
x + 3 = 5
first we need to get all the numbers on to one side of the equal sign while the other side has all the variable
in order to do that we need to subtract 3 on both sides
x + 3 = 5
- 3 - 3
and that leaves us with our answer!
x = 2
i hope this helps you :) if you need anymore help or if i did something wrong then please tell me! have a good day :)
What is the slope of a line perpendicular to the line whose equation is
3x + 3y = 45
Answer:
3(x+y)=45
x+y=15
y=-1x +15
so
slope(m) = -1
Please help me in this!!!!!!
Answer:
Lower (or First) Quartile = 15
Step-by-step explanation:
Answer:
15 I think
Step-by-step explanation:
been a while since I did that but I think 15
Which table represents a linear function?
Table one represents a linear function for the given data.
What is a linear function?A linear function is a mathematical function that can be written in the form:
y = mx + b
where "m" and "b" are constants, and "x" and "y" are variables.
In this form, "m" represents the slope of the line, and "b" represents the y-intercept, the point where the line crosses the y-axis. The slope of the line is the rate of change of the function, representing how much the value of "y" changes for every unit change in "x".
The given table is,
x y
1 5
2 10
3 15
4 20
5 25
The slope of the given data is,
m = ( 10 - 5 ) / ( 2 - 1 ) = 5
m = ( 15 - 10 ) / ( 3 - 2 ) = 5
m = ( 20 - 15 ) / ( 4 - 3 ) = 5
Here the slope is constant, so the function is linear.
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You are given two pairs of triangles. For the first pair of triangles, each side and angle of one triangle is congruent to the corresponding side and angle of the other. You show that rigid motions can transform one triangle so that it matches up with the other. For the second pair of triangles, you show that rigid motions can transform one triangle so that each angle or side of one triangle matches exactly with a corresponding angle or side of the other triangle. What have you proved?
Options:
a) If corresponding pairs of sides and corresponding pairs of angles of two triangles are congruent, then the triangles can be matched up exactly using rigid motions.
b) If two triangles can be matched up exactly using rigid motions, then the corresponding pairs of sides and corresponding pairs of angles of the triangles are congruent.
c) Two triangles can be matched up exactly using rigid motions if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
d) If corresponding pairs of sides and corresponding pairs of angles of two triangles are not congruent, then the triangles are not congruent.
Answer:
c) Two triangles can be matched up exactly using rigid motions if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
Step-by-step explanation:
For both pairs of triangles, what you proved is how to use rigid motions (i.e. rigid transformations) to make congruent shapes.
When rigid transformation is applied to a shape, the image (i.e. result) of the transformation produces an exact shape (i.e. equal corresponding angles and corresponding sides), meaning that the side lengths and the angles of the preimage (before transformation) and the image (after transformation) is unaltered.
Option (c) is true
-2x - 5x + 3 - 8 please help
Answer:
-7x - 5
Step-by-step explanation:
Combine like terms.
The question is in the picture.
Answer:
arc CD = 160°
Step-by-step explanation:
The measures of the arcs on the circle = 360° , then
arc CD = 360 - AC - AD = 360 - 3x - 7x = 360 - 10x
--------------------------------------------------------------------------
The measure of the secant- tangent angle ABC is half the difference of the intercepted arcs, that is
[tex]\frac{1}{2}[/tex] (7x - 3x) = 40 ( multiply both sides by 2 to clear the fraction )
7x - 3x = 80
4x = 80 ( divide both sides by 4 )
x = 20
Then
CD = 360 - 10x = 360 - 10(20) = 360 - 200 = 160°
67% of 200 please give me the answer
Answer: 134
(Hope this helped with whatever you needed it for <3)