The condition imposed on the constants k₁ and k₂ for k₁Θ⁻₁ + k₂Θ⁻₂ to be an unbiased estimator of θ is that their sum must equal 1.
For k₁Θ⁻₁ + k₂Θ⁻₂ to be an unbiased estimator of θ, its expected value should be equal to θ. In other words, we want to find the conditions on k₁ and k₂ such that E(k₁Θ⁻₁ + k₂Θ⁻₂) = θ.
Given that Θ⁻₁ and Θ⁻₂ are unbiased estimators of θ, we have:
E(Θ⁻₁) = θ
E(Θ⁻₂) = θ
Now, let's calculate the expected value of k₁Θ⁻₁ + k₂Θ⁻₂:
E(k₁Θ⁻₁ + k₂Θ⁻₂) = k₁E(Θ⁻₁) + k₂E(Θ⁻₂)
Since E(Θ⁻₁) = θ and E(Θ⁻₂) = θ, we can substitute these values into the equation:
E(k₁Θ⁻₁ + k₂Θ⁻₂) = k₁θ + k₂θ
To make sure this expression is equal to θ, we need:
k₁θ + k₂θ = θ
This implies that k₁ + k₂ = 1. Therefore, the condition imposed on the constants k₁ and k₂ for k₁Θ⁻₁+ k₂Θ⁻₂ to be an unbiased estimator of θ is that their sum must equal 1.
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3. The angle between two equal sides of an isosceles triangle is 52º.
Each of the equal sides is 18 cm long.
a) Determine the measures of the two equal angles in the triangle.
b) Determine the length of the third side.
c) Determine the perimeter of the triangle.
Answer:
a) 64° each
b) 15.78 cm
c) 51.78 cm
Step-by-step explanation:
a) (180 - 52)/2 = 64°
b) cos 64 = x/18, x = 7.89, 2x = 15.78 cm
c) 18 + 18 + 15.78 = 51.78 cm
Thomas loaned $6,250 to Cameron at a simple interest rate of 4.12% p.a. for 2 years and 6 months. Calculate the amount of interest charged at the end of the term. Round to the nearest cent
The amount of interest charged at the end of the term is approximately $644.75.
To calculate the amount of interest charged at the end of the term, we can use the simple interest formula:
Interest = Principal * Rate * Time
Principal = $6,250
Rate = 4.12% = 0.0412 (decimal form)
Time = 2 years + 6 months = 2.5 years
Plugging in these values into the formula, we have:
Interest = $6,250 * 0.0412 * 2.5
Calculating this expression:
Interest = $6,250 * 0.0412 * 2.5 = $644.75
Therefore, the amount of interest charged at the end of the term is $644.75 (rounded to the nearest cent).
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a rectangular field 50m wide and ym long requires 260m fencing. find y
Answer:
5.2m
Step-by-step explanation:
If the angles
are represented in degrees, find both angles:
sin(x + 7) = cos(4x + 8)
Answer:
x = -1/3
Step-by-step explanation:
We have,
sin(x + 7) = cos(4x + 8)
We need to find the value of x.
We know that,
sin(90-x) = cosx
So,
sin(90-(x + 7)) = cos(4x + 8)
cos(x+7) = cos(4x + 8)
i.e.
(X+7) = (4x+8)
7-8 = 4x-x
-1 = 3x
x = -1/3
Answer:
sin(22 ∘ ) = cos(68∘ )
Step-by-step explanation:
Sin(x+7)=cos(4x+8)
(x+7) + (4x+8) = 90
x + 7 + 4x + 8 = 90
5x + 15 = 90
−15 = −15
5x/5 = 75/5
x = 15
Answer: sin(22 ∘ ) = cos(68∘ )
Think about comparing a table to a graph. What steps would you take to determine which of the two has a greater rate of change?
Please help I need this for math!!!Thank you
For the following estimated CAPM (Capital Assets Pricing Model) model for stock XYZ, stock XYZ return = 0.003 + 1.38 (market return) what is the financial interpretation of 1.38 inn nauation of X and Y
In the Capital Asset Pricing Model (CAPM), the coefficient of the market return is known as the stock’s beta. Beta measures the stock’s systematic risk, or its sensitivity to market movements.
what is the financial interpretation of 1.38 inn nauation of X and YA beta of 1 indicates that the stock’s return moves with the market. A beta greater than 1 indicates that the stock is more volatile than the market, while a beta less than 1 indicates that the stock is less volatile than the market.
In this case, the estimated CAPM model for stock XYZ has a beta of 1.38. This means that stock XYZ is expected to be more volatile than the market. For every 1% increase in the market return, stock XYZ’s return is expected to increase by 1.38%. Conversely, for every 1% decrease in the market return, stock XYZ’s return is expected to decrease by 1.38%.
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Antonio has six white socks, two black socks, and four gray socks in a drawer. If he randomly chooses a sock from the drawer, what is the probability he will choose a gray sock?
A.1/12
B.1/4
C.1/3
D.1/2
Answer:
C
Step-by-step explanation:
The probability is 1/3
Arthur is interested in the effects of sleep deprivation usage on number of calories consumed. He asks a group of 20 college students to spend the night in the sleep lab under one of these conditions: no sleep, 2 hours of sleep, 4 hours of sleep, 6 hours of sleep, or 8 hours of sleep. Arthur measures how many calories are consumed by the students in the sleep lab, which is stocked with various food items. After collecting these data, Arthur performs an ANOVA and finds that he can reject the null hypothesis. On the basis of this, what does Arthur know
Answer:
Arthur knows that there is a difference among the groups somewhere, but he does not know where
Step-by-step explanation:
An ANOVA test is a test to find out whether the results of an experiment or a survey are significant or not. ANOVA test helps the researcher or the experimenter to decide whether they reject the null hypothesis or accept the alternate hypothesis in the experiment. In ANOVA test, the experimenter wants to find if there is a difference between them or not.
In the context, Arthur is doing a study and he wishes to find out effect of a sleep deprivation on the number of the calories that people consumed. He collects some data from his subject group from the sleep lab and after running the ANOVA test, he finds out that he can reject the null hypothesis. So on this basis, Arthur knows that there is some basic difference among the members of the group somewhere, but he does not know where actually the difference is.
help would be really nice here just a bit lost
determine Sn given the series: 45 - 56 + 67 - 78 + 89
- 100 + ..... - 342
The given series is an alternating series with a pattern of adding and subtracting consecutive terms. To determine Sn, we need to find the sum of the first n terms of the series. Therefore, the sum of the series is -13,365.
In the given series, each term is obtained by adding 11 to the previous term and then changing its sign. We can observe that the first term is positive (45), the second term is negative (-56), the third term is positive (67), and so on.
To find Sn, we need to determine the number of terms in the series and then calculate the sum. The series ends with -342, so we need to find the position of -342 in the series.
To do this, we can subtract 45 from -342 and divide the result by 11 to find the number of terms. (-342 - 45) / 11 = -297 / 11 = -27. Therefore, the series consists of 27 terms.
To find the sum of the first 27 terms, we can use the formula for the sum of an arithmetic series: Sn = (n/2)(a + l), where n is the number of terms, a is the first term, and l is the last term.
Using the formula, we can calculate Sn as follows: Sn = (27/2)(45 - 342) = (27/2)(-297) = -13,365.
Therefore, the sum of the series is -13,365.
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A quantitatively savvy, young couple is interested in purchasing a home in southern Sydney. They collected data on 48 houses that had recently sold in the area. They want to predict the selling price of homes (in thousands of dollars) based on the size of the home (in square feet).
The regression equation is House Price (in thousands) = 17.1 + 0.0643 Size (sq. ft.)
Predictor Coef SE Coef T P
Constant 17.06 24.59 0.69 0.491
Size (sq. ft.) 0.06427 0.01224 5.25 0.000
S = 48.5733 R-Sq = 37.5% R-Sq(adj) = 36.1%
Use the computer output to test the slope, at the 5% level, to determine whether size (in square feet) is an effective predictor of the selling price of recently sold homes. Include all details of the test.
a) What are the null (H) and alternative hypotheses (Ha) ?
b) What is the t-test statistics?
c) degree of freedom for this t-test statistics?
d) final conclusion of this test is ?
Since the p-value is less than the significance level of 0.05, we can reject the null hypothesis, the size of the home is a significant predictor of the selling price of homes sold recently in the southern Sydney area.
(a) Null hypothesis: H0: β1 = 0 (The size of the home is not a significant predictor of the selling price of homes sold recently).
Alternative hypothesis: Ha: β1 ≠ 0 (The size of the home is a significant predictor of the selling price of homes sold recently).
(b) The t-test statistic: We can use the t-test statistic to test whether the slope (β1) of the regression line is significant at the 5% level.
t = (β1 - 0) / SE(β1)
= 0.0643 / 0.01224
= 5.25
(c) The degrees of freedom (df) for this t-test statistic will be n - 2, where n is the sample size.
Since the sample size is 48, the degrees of freedom will be 48 - 2 = 46.
(d) Final conclusion of this test: Since the p-value is less than the significance level of 0.05, we can reject the null hypothesis.
Thus, we conclude that the size of the home is a significant predictor of the selling price of homes sold recently in the southern Sydney area.
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Solve the following system of IVP: [3 -1 01 7 x' = Ax where A = 4 -2 0 and x(0) = 10x -4 21 Hint: The eigenvalues are λ₁ = -1,A₂ = 2, A3 = 2.
For the given system of initial value problem,
A₁ = 7,
A₂ = -1, and
y = 2exp(-t),
To solve the given system of initial value problem (IVP) with the matrix equation x' = Ax, where A is the given matrix and x(0) = [10, -4, 21], we can use the eigenvalue-eigenvector method.
The matrix A is given as:
A = | 4 -2 0 |
| 3 -1 0 |
| 1 7 2 |
Let's find the eigenvalues and eigenvectors of matrix A.
To find the eigenvalues, we solve the characteristic equation:
det(A - λI) = 0
Substituting the values, we get:
| 4-λ -2 0 |
| 3 -1-λ 0 |
| 1 7 2-λ |
Expanding the determinant, we have:
(4-λ)[(-1-λ)(2-λ)] + 2[3(2-λ) - (-1-λ)7] = 0
Simplifying and solving the equation, we find the eigenvalues:
λ₁ = -1
λ₂ = 2
λ₃ = 2
Next, let's find the corresponding eigenvectors.
For λ₁ = -1:
(A + I)v₁ = 0
| 5 -2 0 | | v₁₁ | | 0 |
| 3 -1 0 | * | v₁₂ | = | 0 |
| 1 7 1 | | v₁₃ | | 0 |
Solving the system of equations, we find the eigenvector corresponding to λ₁:
v₁ = | 2 |
| 5 |
|-1 |
For λ₂ = 2:
(A - 2I)v₂ = 0
| 2 -2 0 | | v₂₁ | | 0 |
| 3 -3 0 | * | v₂₂ | = | 0 |
| 1 7 0 | | v₂₃ | | 0 |
Solving the system of equations, we find the eigenvector corresponding to λ₂:
v₂ = | 1 |
| 1 |
|-1 |
For λ₃ = 2:
(A - 2I)v₃ = 0
| 2 -2 0 | | v₃₁ | | 0 |
| 3 -3 0 | * | v₃₂ | = | 0 |
| 1 7 0 | | v₃₃ | | 0 |
Solving the system of equations, we find the eigenvector corresponding to λ₃:
v₃ = | 2 |
| 3 |
| 1 |
Now that we have the eigenvalues and eigenvectors, we can write the general solution to the system of differential equations as:
x(t) = c₁ * exp(λ₁ * t) * v₁ + c₂ * exp(λ₂ * t) * v₂ + c₃ * exp(λ₃ * t) * v₃
Substituting the given initial condition x(0) = [10, -4, 21], we can find the specific solution by solving the following system of equations:
c₁ * v₁ + c₂ * v₂ + c₃ * v₃ = x(0)
Substituting the values of the eigenvectors and the initial condition, we get:
2c₁ + c₂ + 2c₃ = 10 (Equation 1)
5c₁ + c₂ + 3c₃ = -4 (Equation 2)
-c₁ - c₂ + c₃ = 21 (Equation 3)
Solving this system of equations will give us the values of c₁, c₂, and c₃, which will determine the specific solution.
By solving Equations 1, 2, and 3, we find:
c₁ = 1
c₂ = -5
c₃ = -3
Therefore, the specific solution to the initial value problem is:
x(t) = exp(-t) * | 2 | + exp(2t) * | 1 | + exp(2t) * |-3 |
| 5 | | 1 |
|-1 | | 1 |
Simplifying this expression, we get:
x(t) = | 2exp(-t) + 5exp(2t) - 3exp(2t) |
| 5exp(-t) + exp(2t) + exp(2t) |
|-exp(-t) + exp(2t) + exp(2t) |
Finally, we can rewrite the solution in the given form (7) - ₁ (1) ¹²+₂ (1) ¹:
x(t) = 7 * | 2exp(-t) | + (-1) * | 5exp(-t) |
| 5exp(-t) | | -exp(-t) |
Therefore, A₁ = 7, A₂ = -1, and y = 2exp(-t).
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Enteros 15+18 resultado
HELPPPPPPPPP
What is the value of x in the figure at the right?
Answer:
x=30
HOPE THIS HELPS
-Todo <3
Step-by-step explanation:
60=2x
/2 /2
30=x
Can y’all help me?
The teacher wants me to do work but ion understand this bc Ian done school for 3 months so I’m a bit behind...
Answer:
402.1 in^2
Step-by-step explanation:
Find the area of the circle with the 18 in. radius first.
Formula for a circle is πr^2
So the area of the circle with the 8 in. radius is 1017.9 in^2
Now do the same for the 14 in. radius circle.
The area for the 14 in. radius circle is 615.8
Now subtract:
1017.9 - 615.8 =
402.1 in^2
hope this helped!
If 40% of a number is 14, find 20% of that number.
Answer:
7
Step-by-step explanation:
Because half of 40% is 20%
So 14%2 = 7
Simplify the following and leave your answer in smallest form
1 + 2 + 1
_ _ _
2 3 6
Answer:
1/59
Step-by-step explanation:
Answer:
1/59
think of it dude
Uhhh someone plz help me plz
Answer:
The number 3.97 is very close to the whole number 4. Therefore, the difference of 4.3 - 3.97 is about 0.33. So, the difference of 4.3 - 3.97 is less than 1.
Remember: The farther the number is to the right, the smaller it becomes.
Ex. 0.10 is greater than 0.100 since the number is shorter and closer to the ones/whole number spot.
Hope this Helps!:)
What is the measure of angle R? *
7 points
R
(10n + 19)"
(12n - 4)
S
Answer:
(10n + 19) (12n - 4)º ... The midsegment of a trapezoid is parallel to each base and its measure is one half the ...
Missing: pointsR( S
Step-by-step explanation:
someone help me ill mark you brainliest x
Answer:
x= 64° y= 18° z= 98°
Step-by-step explanation:
x= 64°
y = 18°
z = 180° - x - y
z = 180° - 64° - 18°
z= 98°
What is the mean of the following data set?
25, 34, 33, 41, 19, 20, 25, 22, 30, 29, 34, 39
A: 29.5
B:29.25
C:29.75
Answer:
B
Step-by-step explanation:
After adding them all together, we end up with 351. There are 12 numbers, so we do 351/12, getting 29.25.
NO LINKS PLEASE
SOMEONE HELP IM DESPERATE
FIND THE EXACT VALUE OF EACH TRIGONOMETRIC FUNCTION USING THE UNIT CIRCLE
Answer: 45
Step-by-step explanation: 360-315=45
Skip count 89300 forward by 5000
A closed plain forgive with all sides congruent and all angles congruent is called a
Answer:
Polygon. A closed plane figure for which all sides are line segments. The name of a polygon describes the number of sides. A polygon which has all sides mutually congruent and all angles mutually congruent is called a regular polygon.
please solve for x!!!
Answer:
2x+156=4x+192
192-156=-4x+2x
36=-2x
x=-18
Step-by-step explanation:
can someone please help me with this question?
Answer:
your answer will be 70 have a nice day:)
Step-by-step explanation:
43+27=70
Answer: 18
Step-by-step explanation:
To answer this question you have to add all the number and however many over 100 there is that how many like both of the teams so 27 + 48 + 43 = 118
then you take 100 away from 118 and you get 18
If the two triangles are similar,what is the length of the missing side?
Answer:
8 m
Step-by-step explanation:
7.5 - 1.5 = 6
2 + 6 = 8
Find –(–14).
–14
–4
4
14
Answer:
bhjtijo3
Step-by-step explanation:
Answer:
Step-by-step explanation:
D. 14
please help___________
WORTH 25 POINTS! HELP PLZZZZZZ
Answer:
I pretty sure its A
Step-by-step explanation:
Answer:
The answer on the top, 32 * __ = 3616
Step-by-step explanation:
3616/32 = __
multiply by 32
3616 = 32 * __ or 32 * __ = 3616