A sufficient statistic for the parameters (μ, λ) is T(X) = (T1(X), T2(X)) where T1(X) = Σ Xi^(-1) and T2(X) = Π Xi.
To find a sufficient statistic for (μ,λ), we can use the factorization theorem which states that a statistic T(X) is sufficient for a parameter θ if and only if the joint probability distribution of X can be factorized as follows
f(x∣θ) = g[T(x)∣θ]h(x)
where g and h are non-negative functions that do not depend on θ.
Using the given probability density function, we have
f(x∣μ,λ) = (λ/2πx^3)^(1/2)exp[−λ(x-μ)^2/(2μ^2 x) ]
= [(λ/2π)^(1/2)/x^(3/2)] exp[−λ(x-μ)^2/(2μ^2 x)]
= [(λ/2π)^(1/2)/x^(3/2)] exp[−(λ/2μ^2) x + (λμ/μ^2) x^(-1)]
= [exp(λμ/μ^2)/(2πλ)^(1/2)] [x^(-3/2) exp(−λ/2μ^2 x)]
Let's define two functions as follows
T1(X) = Σ Xi^(-1)
T2(X) = Π Xi
Then, we can write the joint pdf of X as follows
f(x1, x2, ..., xn | μ, λ) = [exp(λμ/μ^2)/(2πλ)^(1/2)] [Π xi^(-3/2) exp(−λ/2μ^2 xi)]
= [exp(λμ/μ^2)/(2πλ)^(1/2)] [Π xi^(-3/2)] [exp(−λ/2μ^2 Σ xi)]
Notice that the term [Π xi^(-3/2)] does not depend on (μ, λ), and can be factored out. Therefore, the joint pdf can be rewritten as
f(x1, x2, ..., xn | μ, λ) = [Π xi^(-3/2)] [exp(λμ/μ^2)/(2πλ)^(1/2)] [exp(−λ/2μ^2 Σ xi)]
= g(T1(X), T2(X) | μ, λ) h(X)
where g(T1(X), T2(X) | μ, λ) = [exp(λμ/μ^2)/(2πλ)^(1/2)] [exp(−λ/2μ^2 Σ xi)] and h(X) = [Π xi^(-3/2)].
Learn more about probability density function here
brainly.com/question/31039386
#SPJ4
The given question is incomplete, the complete question is:
Let X1,…,Xn be i.i.d. random variables with the inverse Gaussian distribution having pdf is given by f(x∣μ,λ)= (λ/2πx^3)^(1/2)exp[−λ(x-μ)^2/(2μ^2 x) ] 0 <x <∞, Find a sufficient statistic for
(μ,λ)
ompute the amount to be paid for each of the four separate invoices assuming that all invoices are paid within the discount period. Terms Payment $ Merchandise (gross) a. $ 8,000 24,500 C. 81,000 17,500 I 2/10, n/60 1/15, EOM 1/10, n/30 3/15, n/45 7,840 20,825 72,900 14,875
Where the above Terms exists, the amount to be paid in each of the above invoices are given as follows;
Invoice 1: $7,840Invoice 2: $24,255Invoice 3: $80,190Invoice 4: $16,975.How would one define the the Terms above?Note that the terms are defined as follows;
Terms A: 2/10, n/60 (2% discount if paid within 10 days, net due in 60 days)
Terms B: 1/15, EOM (1% discount if paid within 15 days, end of month terms)
Terms C: 1/10, n/30 (1% discount if paid within 10 days, net due in 30 days)
Terms D: 3/15, n/45 (3% discount if paid within 15 days, net due in 45 days.
So to compute the amount to be paid for each of the four separate invoices assuming that all invoices are paid within the discount period, we need to calculate the amount of the discount and subtract it from the gross merchandise amount.
For terms 2/10, n/60:
Discount = 2% of $8,000 = $160
Amount to be paid = $8,000 - $160
= $7,840
For terms 1/15, EOM:
Discount = 1% of $24,500 = $245
Amount to be paid = $24,500 - $245
= $24,255
For terms 1/10, n/30:
Discount = 1% of $81,000 = $810
Amount to be paid = $81,000 - $810
= $80,190
For terms 3/15, n/45:
Discount = 3% of $17,500 = $525
Amount to be paid = $17,500 - $525
= $16,975
Therefore, the amount to be paid for each of the four separate invoices assuming that all invoices are paid within the discount period are:
Learn more about Payment terms:
https://brainly.com/question/24086159
#SPJ1
A simple random sample with n = 25 provided a sample mean of 30 and a sample standard deviation of 4. Assume the population is approximately normal. a. Develop a 90% confidence interval for the population mean. b. Develop a 95% confidence interval for the population mean. c. Develop a 99% confidence interval for the population mean. d. What happens to the margin of error and the confidence interval as the confidence level is increased?
Conversely, as the confidence level decreases, the margin of error becomes smaller, and the confidence interval becomes narrower.
What is confidence interval?In statistics, a confidence interval is a range of values that is likely to contain the true value of a population parameter (such as a mean or a proportion), based on a sample from that population. The confidence interval is typically expressed as an interval around a sample statistic, such as a mean or a proportion, and is calculated using a specified level of confidence, typically 90%, 95%, or 99%.
Here,
To develop a confidence interval, we need to use the following formula:
Confidence Interval = sample mean ± margin of error
where the margin of error is calculated as:
Margin of Error = z* (sample standard deviation/ √n)
where z* is the critical value from the standard normal distribution table based on the chosen confidence level.
a. For a 90% confidence interval, the critical value (z*) is 1.645. Thus, the margin of error is:
Margin of Error = 1.645 * (4 / √25) = 1.317
So, the 90% confidence interval for the population mean is:
30 ± 1.317, or (28.683, 31.317)
b. For a 95% confidence interval, the critical value (z*) is 1.96. Thus, the margin of error is:
Margin of Error = 1.96 * (4 / √25) = 1.568
So, the 95% confidence interval for the population mean is:
30 ± 1.568, or (28.432, 31.568)
c. For a 99% confidence interval, the critical value (z*) is 2.576. Thus, the margin of error is:
Margin of Error = 2.576 * (4 / √25) = 2.0656
So, the 99% confidence interval for the population mean is:
30 ± 2.0656, or (27.9344, 32.0656)
d. As the confidence level increases, the margin of error also increases, because we need to be more certain that our interval includes the true population mean. This means that the confidence interval becomes wider as the confidence level increases.
To know more about confidence interval,
https://brainly.com/question/28969535
#SPJ1
need some help on some questions
For the triangle ABC, the given trigonometric ratios are -
a. sin A = 8/17
b. cos A = 15/17
c. tan A = 8/15
d. tan B = 8/15
What is trigonometric ratio?
Triangle side length ratios are known as trigonometric ratios. In trigonometry, these ratios show how the ratio of a right triangle's sides to each angle. Sine, cosine, and tangent ratios are the three fundamental trigonometric ratios.
For a right-angled triangle ABC, the hypotenuse AB is given as 17.
The base CB is given as 15 and the perpendicular AC is given as 8.
The angle C is given to be 90°.
Using the given values of the sides of the right triangle ABC, we can calculate the trigonometric ratios as follows -
a. sin A = opposite/hypotenuse = AC/AB = 8/17 (reduced fraction)
b. cos A = adjacent/hypotenuse = CB/AB = 15/17 (reduced fraction)
c. tan A = opposite/adjacent = AC/CB = 8/15 (reduced fraction)
d. tan B = opposite/adjacent = AC/CB = 8/15 (reduced fraction)
Note that since angle C is 90°, angles A and B are acute angles, so their tangent ratios are equal to each other.
Therefore, the ratios expressed as reduced fractions are -
a. sin A = 8/17
b. cos A = 15/17
c. tan A = 8/15
d. tan B = 8/15
To learn more about trigonometric ratio from the given link
https://brainly.com/question/13276558
#SPJ1
Cameron aces all her exams. However, she blows off the homework, quizzes and class participation her score for the semester were:
Exam 1: 93/100
Exam 2: 95/100
Exam 3: 90/100
Exam 4: 89/100
Homework: 10/100
Quizzes: 14/100
Participation: 50/100
Cameron‘s teacher assigns final grades using a standard scale ( 90% is A, 80% is a B, 70% is a C, 60%is a D) if Cameron’s teacher uses the points system for averaging final grades where you add up all of the points earned and divide by the points possible in the course what grade did she get in the class?
A, B, C, D
Answer:
D
Step-by-step explanation:
TO find the average, add all scores, and divide by the number of scores.
93+95+90+89+10+14+50=441 divided by 7=63. That is a D.
In which number is the figit 8 ten times it is in the number 18?
Answer:
Let's call the number we are looking for "x". We are told that the digit 8 appears ten times as often in "x" as it does in 18.
The digit 8 appears once in the number 18, so it must appear 10 times in "x".
Let's count the number of 8's in "x" in terms of the number of digits of "x".
If "x" has 1 digit, then it cannot have 10 8's, so we can rule out this case.
If "x" has 2 digits, then the maximum number of 8's it can have is 9 (e.g., 88). This is still not enough, so we can rule out this case as well.
If "x" has 3 digits, then the maximum number of 8's it can have is 27 (e.g., 888), which is enough.
Therefore, the number we are looking for is a 3-digit number that contains 10 8's. We can write such a number as:
x = 888x8x8x8
where "x" can be any digit other than 8.
Note that there are other 3-digit numbers that contain 10 8's, but this is one possible solution.
(please mark my answer as brainliest)
A box contains ten cards labeled j, k, l, m, n, o, p, q, r, and s. One card will be randomly chosen. What is the probiability of choosing a letter from n to q
The probability of choosing a letter from n to q would be = 2/5
What is probability ?Probability is defined as the expression that is used to represent the possibility of an outcome of an event which can be solved with the formula = chosen events/ total outcomes.
The number of cards in the box = 10
The various cards are labelled as follows= j, k, l, m, n, o, p, q, r, and s.
The number of cards from n to q = 4
Therefore the probability that a number from n to q will be chosen = 4/10 = 2/5.
Learn more about probability here:
https://brainly.com/question/25688842
#SPJ1
PLEASE HELP YOU WILL BE BRAINIEST!!! Use the chart!!!!
The researchers decided to construct a confidence interval to determine if the difference of the means is significant. To determine whether the confidence interval would be reliable they create Q-Q plots of both random samples and see that they are approximately normal. Are the requirements for constructing a confidence interval satisfied? Why or why not? a. Yes. The distribution of the mean for each sample is normal since the researchers can apply the Central Limit theorem. b. Yes. The distribution of the mean of each sample is normal since the data have been determined to be normal. c. No. The distribution of the mean of each sample is not normal since the sample size is not large enough. d. No. The company needs to check that all the data combined is normal. 3. Of the four types of confidence intervals listed below, which one is appropriate for this experiment? a. Confidence interval for μ when σ is known. b. Confidence interval for μ when σ is unknown. c. Confidence interval for the mean of differences, using dependent samples. d. Confidence interval for the difference of means, using independent samples.
a. Not satisfied based on Central Limit Theorem alone. b. Satisfied if Q-Q plots show approximately normal distribution. c. Sample size affects shape of distribution, but no specific cutoff for normality. d. Appropriate interval: difference of means using independent samples.
a. No. While the Central Limit Theorem applies to the mean of a sufficiently large sample, it does not guarantee that the underlying distribution is normal.
b. Yes. If the Q-Q plots of both random samples show that they are approximately normal, then the assumption of normality is satisfied for constructing a confidence interval for the difference of means.
c. No. The size of the sample does affect the shape of the sampling distribution, but there is no specific sample size cutoff for normality.
d. Yes. The appropriate confidence interval for this experiment is the confidence interval for the difference of means, using independent samples, since the samples are assumed to be independent.
Learn more about Central Limit Theorem here: brainly.com/question/18403552
#SPJ4
4) 6 out of the 80 dogs in a shelter were adopted yesterday. Express adopted rate as a percent.
Answer:
Step-by-step explanation:
To find the adoption rate as a percentage, we need to divide the number of dogs adopted by the total number of dogs in the shelter, then multiply by 100.
adoption rate = (dogs adopted / total dogs) * 100%
adoption rate = (6 / 80) * 100%
adoption rate = 0.075 * 100%
adoption rate = 7.5%
Therefore, the adoption rate as a percent is 7.5%.
Whenever we construct a confidence interval for the population mean, the margin of error includes the standard error of x bar and theA. sampling biasB. nonresponse biasC. z or t value associated with a 95% confidence levelD. desired level of confidence
The margin of error in a confidence interval for the population mean includes the standard error of the sample mean and the z or t value associated with a certain level of confidence, usually 95% or 99%. Therefore, the correct answer is (C).
Sampling bias and nonresponse bias are potential sources of error in survey or study design and data collection, but they are not directly related to the construction of a confidence interval.
The desired level of confidence is a key input for determining the z or t value used in the calculation of the margin of error, but it is not included in the margin of error itself. The correct answer is z or t value associated with a 95% confidence level.
So, the correct option is (C).
To know more about confidence interval:
https://brainly.com/question/24131141
#SPJ4
NEED HELPPPP PLSSSS
DUE TOMORROW!!
8.The method that resulted in Garcia winning might not be fair to the other nominees because it does not account for their individual achievements or skill sets.
What is nominees ?Nominees are individuals or organizations that have been selected or chosen from a given group to represent them in a certain process or event. Nominees are usually chosen for their proficiency, expertise, or reputation in a certain field or area. For example, in some elections, political parties nominate individuals to represent them in the election and these nominees are then voted upon by the public. Similarly, some organizations nominate a particular individual or group of individuals to represent them in awards or recognition ceremonies for their excellence and achievements.
It simply rewards the nominee with the most votes, regardless of their ability or accomplishments. This could lead to someone who is less qualified or experienced receiving the award, while the more deserving candidates are overlooked.
To learn more about nominees
https://brainly.com/question/17268004
#SPJ1
explain why a set in r5 ust be linearly independent when is linearly indedependent and v4 is not in span
A set in R⁵ must be linearly independent because of the dimensionality of the space.
A Set of vectors in R⁵, the five-dimensional Euclidean space, must be linearly independent because of the dimensionality of the space.
The maximum number of linearly independent vectors in any set in R⁵ is 5 since any set with more than 5 vectors would necessarily contain a linearly dependent subset.
This is because any vector in R⁵ can be expressed as a linear combination of at most 5 linearly independent vectors, as the dimension of R⁵ is 5.
Therefore, any set with more than 5 vectors would have at least one vector that could be written as a linear combination of the other vectors in the set, making the set linearly dependent.
Learn more about Linearly Independent Sets here
https://brainly.com/question/29646890
#SPJ4
The given question is incomplete, the complete question is
Explain why a set in R⁵ must be linearly independent.
Find the maximum/minimum value of the quadratic function q² + 22q = y - 85 by
completing the square method.
O-36
O-48
C
-24
-64
Step-by-step explanation:
To find the maximum/minimum value of the quadratic function q² + 22q = y - 85, we can complete the square as follows:
q² + 22q = y - 85
q² + 22q + 121 = y - 85 + 121 (adding (22/2)² = 121 to both sides)
(q + 11)² = y + 36
Now, we have a square of a binomial on the left side, which means the minimum value of the quadratic function is y + 36, and it occurs when (q + 11) = 0. Thus, the minimum value is:
y + 36 = 36 - 85 = -49
Similarly, the maximum value of the quadratic function occurs when (q + 11) = 0, but this time the value of y will be as large as possible. The largest possible value of y occurs when STU is a permutation of the digits 9, 8, and 7 (since PQR must be 4, 0, and 3 in some order). Thus, the maximum value is:
y + 36 = 9 + 8 + 7 - 85 + 36 = -25
Therefore, the options are incorrect and the correct answers are:
Minimum value: -49
Maximum value: -25
sonny's select the options that will create the correct equation of the estimated population regression line.
The equation of the estimated population regression line is typically written in the form:
y = a + bx
where:
y is the dependent variable (or response variable)
x is the independent variable (or predictor variable)
a is the intercept (the value of y when x = 0)
b is the slope (the change in y for a unit change in x)
To create the correct equation of the estimated population regression line, Sonny should select the following options:
The variable y should be the dependent variable (or response variable).
The variable x should be the independent variable (or predictor variable).
The estimated intercept value should be plugged into the equation for a.
The estimated slope value should be plugged into the equation for b.
So, the correct equation of the estimated population regression line would be:
y = a + bx
where a and b are the estimated intercept and slope values, respectively.
To know more about Regression:
https://brainly.com/question/11805375
#SPJ4
please help!! its for homework that is due very soon!!
Answer:
A>C>B
Step-by-step explanation:
The angle facing or opposite the longest side is the largest angle while.............
whats the radius of the button
Answer:
2.5
Step-by-step explanation:
diameter is 5 and the radius is half of the diameter so it is 2.5
hope this helps :)
This problem explores some questions regarding the fishery model
dt
dP
=P(1−P)−h
If you have not yet run the Jupyter notebook please do so now. Find analytical expressions for the two fixed points of the model, in terms of
h
. Give an expression for the stable fixed point. You may assume that the larger fixed point is the stable one. For what values of
h
does there exist a fixed point?
a) The expression for the stable fixed point is P* = (1 + sqrt(1 - 4h)) / 2
b) There exists a fixed point for all values of h less than or equal to 1/4.
The fixed points of the model are the values of P at which dP/dt = 0. Therefore, we need to solve the equation
P(1-P) - h = 0
Expanding the left-hand side, we get
P - P^2 - h = 0
Rearranging, we get a quadratic equation
P^2 - P + h = 0
Using the quadratic formula, the two solutions for P are
P = (1 ± sqrt(1 - 4h)) / 2
a) The larger root is the stable fixed point, as it corresponds to a minimum of the fish population growth function. Therefore, the expression for the stable fixed point is
P* = (1 + sqrt(1 - 4h)) / 2
b) For the model to have a fixed point, the quadratic equation must have real roots. This occurs when the discriminant (the expression inside the square root) is non-negative
1 - 4h ≥ 0
Solving for h, we get
h ≤ 1/4
Learn more about quadratic equation here
brainly.com/question/30098550
#SPJ4
The given question is incomplete, the complete question is:
This problem explores some questions regarding the fishery model
dP/dt =P(1−P)−h
If you have not yet run the Jupyter notebook please do so now. Find analytical expressions for the two fixed points of the model, in terms of h
a) Give an expression for the stable fixed point. You may assume that the larger fixed point is the stable one. b) For what values of h does there exist a fixed point?
The Venn diagram here shows the cardinality of each set. Use this to find the cardinality of the given set.
n(A)=
The cardinality of set A, n(A) = 29
What is cardinality of a set?The cardinality of a set is the total number of elements in the set
Given the Venn diagram here shows the cardinality of each set. To find the cardinality of set A, n(A), we proceed as follows.
Since the cardinality of a set is the total number of elements in the set, then cardinality of set A , n(A) = 9 + 8 + 3 + 9
= 29
So, n(A) = 29
Learn more about cardinality of a set here:
https://brainly.com/question/27846845
#SPJ1
How do you solve this equation?
Solved equation x=80 and z=2, y=40
What is Variables?An element, feature, οr factοr that is liable tο vary οr change
If y varies directly as x and inversely as the square οf z, we can write the fοllοwing prοpοrtiοnality:
y ∝ x/z²
where ∝ denοtes prοpοrtiοnality cοnstant.
Tο find the value οf ∝, we can use the given values οf y, x, and z:
y = ∝ x/z²
28 = ∝ (63)/(3)²
∝ = 28 * (3)² / (63)
∝ = 4/3
Nοw we can use this value οf ∝ tο find y when x=80 and z=2:
y = ∝ x/z²
y = (4/3) * (80)/(2)²
y = 40
Therefοre, when x=80 and z=2, y=40.
To learn more about Variables, click on the link below:
https://brainly.com/question/29696241
#SPJ1
6x+16=8x-18 i need x
Answer:
x = 17
Step-by-step explanation:
Subtract 6x from both sides:
2x - 18 = 16
Add 18 on both sides to isolate the variable:
2x = 18 + 16
2x = 34
Divide by 2: x = 17
the area of a rectangle is 33.12cm². Given that one side of length is 4.6cm. Find the length of the other side
Answer:
7.2 cm----------------------------
Area of rectangle formula:
A = lwGiven:
A = 33.12 cm²,w = 4.6 cm.Find the missing side length:
l = A/wl = 33.12/4.6l = 7.2 cmAnswer:
7.2cm
Step-by-step explanation:
We are here given that, the area of a rectangle is 33.12cm² and one of the side is 4.6cm .
We are interested in finding the length of the other side,
As we know that the area of rectangle is calculated using the formula,
Area = l * b
where l is the length and b is the breadth.
Now substitute the respective values,
33.12cm² = l * 4.6cm
l = 33.12cm²/4.6cm
l = 7.2 cm
Hence the value of second side is 7.2cm
FILL IN THE BLANK. The population parameters that describe the y-intercept and slope of the line relating y and x, respectively, are _____. Group of answer choices B0 and B1 y and x a and b a and B
The equation for a linear regression model is represented as: y = B0 + B1x + error.
What is Slope ?
Slope refers to the measure of steepness of a line. It is defined as the ratio of the change in the y-coordinate to the change in the x-coordinate between any two points on the line. It is also called the gradient of the line.
In statistics, a linear regression model is used to describe the relationship between a dependent variable (usually denoted as "y") and one or more independent variables (usually denoted as "x").
The equation for a linear regression model is represented as: y = B0 + B1x + error
where B0 is the y-intercept, B1 is the slope of the line relating y and x, and error is the random error term. The population parameters B0 and B1 are the true values of the y-intercept and slope that would be obtained if the entire population were studied, rather than just a sample.
These parameters are estimated using the sample data, and the resulting estimates are used to construct the regression equation. The estimates of the population parameters are based on the assumption that the sample is representative of the population, and that the errors are normally distributed with constant variance.
Therefore, The equation for a linear regression model is represented as: y = B0 + B1x + error
To learn more about Slope from given link.
https://brainly.com/question/3605446
#SPJ1
Determine the number of elements of a set and represent the number of elements using a symbol
We can represent the number of elements in a set using the symbol |A| or n(A). So, we can say |A| = 5 or n(A) = 5. We can make generalizations about the equality of sets based on the definition above.
What is set?In mathematics, a set is a collection of distinct objects, which can be anything such as numbers, letters, or other mathematical objects. These objects are called the elements or members of the set. Sets can be defined using various methods such as listing the elements, describing properties of the elements, or using set-builder notation. For example, we can define the set of even numbers using set-builder notation as {x | x is an integer and x is divisible by 2}. Sets play a fundamental role in various branches of mathematics, including algebra, geometry, and analysis. They are used to define mathematical structures such as groups, rings, and fields, and to study various mathematical concepts such as functions, relations, and cardinality.
Here,
11.1.4 To determine the number of elements of a set, you need to count the number of distinct elements in the set. For example, if you have a set A = {1, 2, 3, 4, 5}, then the number of elements in set A is 5.
11.1.5 Two sets are equal if they have exactly the same elements. For example, if we have set A = {1, 2, 3} and set B = {3, 2, 1}, then A and B are equal sets because they contain the same elements, even though the order of the elements is different. We can write this as A = B. If two sets are not equal, then we use the symbol ≠ to denote inequality. For example, if set A = {1, 2, 3} and set B = {4, 5, 6}, then A ≠ B.
Some of these generalizations are:
Two sets are equal if and only if they have the same elements.
The order of the elements in a set does not matter for equality.
If two sets have different elements, then they are not equal.
If two sets have the same elements, but with different multiplicities, then they are not equal.
To know more about set,
https://brainly.com/question/28492445
#SPJ1
The following table provides a probability distribution for the random variable y. Y f(y) 3 0. 20 5 0. 30 6 0. 40 9 0. 10 (a) Compute Var(y) and sigma. If required round your answer to two decimal places
Var(y) = E(y2) – [E(y)]2
E(y2) = 3² * 0.2 + 5² * 0.3 + 6² * 0.4 + 9² * 0.1 = 68.6
E(y) = 3 * 0.2 + 5 * 0.3 + 6 * 0.4 + 9 * 0.1 = 6.2
Var(y) = 68.6 – 6.22 = 37.44
σ = √Var(y) = √37.44 = 6.11
I will mark you brainiest!
How many polygon types (based on the number of sides in each) are shown in the diagram below?
A) 4
B) 3
C) 2
Answer:
A) 4
Step-by-step explanation:
There are 2 lines dividing the polygon.
The first two on the top are triangles.
The two on the bottom are irregular polygons.
Added up, that's 4 polygons according to the line distribution.
d. Two judges in a beauty contest rank the ten competitors in the following order.
Do d. Two judges in a beauty contest rank the ten competitors in the following order.
Do the two judges appear to agree in their standard? the two judges appear to agree in their standard?
The correlation coefficient is close to zero, we can conclude that the two judges do not appear to agree in their standards.
What is correlation and causation in statistics?Nevertheless, a correlation between two variables does not always imply that a change in one variable is the reason for a change in the values of the other.
There is a causal link between the two occurrences, which means that causation shows that one event is the outcome of the occurrence of the other event. This concept is also known as cause and effect.
For the given ranks for two judges the difference between their ranks is:
d: 0.0 4.0 -2.0 1.0 -0.5 1.5 -1.0 -1.0 0.5 2.0
Squaring the given distance we have:
d²: 0.0 16.0 4.0 1.0 0.25 2.25 1.0 1.0 0.25 4.0
Σd² = 29.75
The Spearman's rank correlation coefficient is given as:
ρ = 1 - (6Σd²)/(n(n²-1))
ρ = 1 - (629.75)/(10(10²-1))
ρ ≈ 0.03
Since the correlation coefficient is close to zero, we can conclude that the two judges do not appear to agree in their standards.
Learn more about correlation here:
https://brainly.com/question/18498382
#SPJ1
The complete question is:
xercise 1.3.4 in each case, either express y as a linear combination of a1, a2, and a3, or show that it is not such a linear combination. here:
Here, y can be expressed as a linear combination of a1, a2, and a3 is y = (-1/8) a1 + (9/4) a2 - (5/2) a3.
We can express y as a linear combination of a1, a2, and a3 if and only if y is a linear combination of the column vectors of the matrix A whose columns are a1, a2, and a3. We can write this as:
y = c1 a1 + c2 a2 + c3 a3
where c1, c2, and c3 are constants to be determined. We can solve for these constants by writing the system of equations in matrix form:
A [c1; c2; c3] = y
where [c1; c2; c3] is a column vector of the constants c1, c2, and c3. We can solve for [c1; c2; c3] by multiplying both sides by the inverse of A (assuming it exists):
[c1; c2; c3] = A^(-1) y
If A^(-1) exists, then y can be expressed as a linear combination of a1, a2, and a3. Otherwise, y cannot be expressed as a linear combination of a1, a2, and a3.
For y = [1 2 4 0], we have:
A = [-1 3 0 1; 3 1 2 0; 1 1 1 1]
We can compute the inverse of A using row reduction:
[A | I] = [-1 3 0 1 | 1 0 0;
3 1 2 0 | 0 1 0;
1 1 1 1 | 0 0 1]
[R2 - 3R1, R3 - R1] = [-1 3 0 1 | 1 0 0;
0 -8 2 -3 | -3 1 0;
0 -2 1 0 | -1 0 1]
[R2 / (-8), R3 + 2R2] = [1/8 -3/8 0 3/8 | 3/8 -1/8 0;
0 1 0 -1/4 | 3/4 -1/4 0;
0 0 1 -1/2 | 1/2 -1/2 1]
Therefore, A^(-1) = [1/8 -3/8 0 3/8;
0 1 0 -1/4;
0 0 1 -1/2;
0 0 0 0]
We can now compute [c1; c2; c3]:
[c1; c2; c3] = A^(-1) y = [1/8 -3/8 0 3/8;
0 1 0 -1/4;
0 0 1 -1/2;
0 0 0 0] [1; 2; 4; 0] = [-1/8; 9/4; -5/2; 0]
Therefore, y as a linear combination of a1, a2, and a3:
y = (-1/8) a1 + (9/4) a2 - (5/2) a3
To know more about linear combination here
https://brainly.com/question/30326131
#SPJ4
_____The given question is incomplete, the complete question is given below:
Exercise 1.3.4 in each case, either express y as a linear combination of a1 = [-1 3 0 1], a2 = [3 1 2 0], and a3= [1 1 1 1], or show that it is not such a linear combination. here: y = [1 2 4 0]
22 and 28 are two numbers Express the smallest number as a percentage of the sum of the two numbers
Answer: 44%
Step-by-step explanation:
22 is the smallest of the two numbers, and you want that number as a percentage of the sum of the two numbers. So basically it is asking you to put 22/(22+28) as a percentage. The step by step is as follows:
1. Simplify denominator
22+28 = 50
2. Rewrite the fraction so that the numerator is out of 100
22/50 = 44/100
3. Convert this new fraction to percentage
44/100= 44%
Hope this helps!!
What is the length of the distance between the two points of (6,-2)
and (3, 4)?
O √13
O √45
O √65
O √117
Answer:
[tex]\sqrt {45}[/tex]
Step-by-step explanation:
Distance between two points, (x1, y1) and (x2, y2) in a 2D cartesian coordinate is given by
[tex]d = \sqrt {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]
here the points are (6, - 2) and (3, 4)
We get
[tex]d = \sqrt {(3 - 6)^2 + (4 - (-2))^2}\\\\d = \sqrt {(-3)^2 + (6)^2}\\\\d = \sqrt {{9} + {36}}\\\\d = \sqrt {45}[/tex]
i need help i forgot how to do this
Step-by-step explanation:
For RIGHT triangles : sin ( angle) = opposite LEG / Hypotenuse
so sin B = 32 / 68 = 8 / 17