Illustrate with a diagram a consumer in equilibrium with indifference curves and a budget constraint. Measure units of X on the horizontal axis and units of Y on the vertical axis. Provide intuitive and mathematical explanations for what must be true in equilibrium.

Answer:

x = 3, y = -1

Step-by-step explanation:

4x - 3y = 15

x + y = 2 -> y = 2 - x

4x - 3(2 - x) = 15

4x - 6 + 3x = 15

7x = 21

x = 3

y = 2 - x

y = 2 -3

y = -1

Answer: x =3, y = -1

Step-by-step explanation:

[tex]\bf{\underline{We\:solve\:by\:applying\:the\:reduction\:method.}}[/tex]

          [tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{The\:exercise\:is \ ---\to \ \left \{ {{4x-3y=15} \atop {x+y=2 \ \ \ \ \ }} \right. } \end{gathered}$}}[/tex]

Multiply the second equation by -4, then add both equations.

  4x - 3y = 15

  -4(x + y = 2)

We add these equations to eliminate x.

    -7y = 7

Then we solve -7y = 7 for y. (We divide by 7)

        [tex]\bf{\dfrac{-7y}{ -7}=\dfrac{7}{-7} } \\ \\ \bf{y=-1}[/tex]

We place the found value of y , in one of the original equations y in order to solve for x:

        4x - 3y = 15

        4x - 3(-1) = 15

        3x + 4 = 15

We add (-3) to both sides.

     4x + 3 + (-3) = 15 + (-3)

      4x = 12

We divide both sides by 4.

         [tex]\bf{\dfrac{4x}{4}=\dfrac{12}{4} } \\ \\ \bf{x=3}[/tex]

Solution: x=3,y=-1

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a. n is 100 and p = 2 when we generate the simulated data set.

b. By generating a scatterplot we found a quadratic function. Y from -9 to 3 and x from -2 to 2.

c. Yes the result is the same as we got in question c.

d. Report of d is exactly the same because LOOCV will be the same since it evaluates n folds of a single observation.

e. The quadratic model and yes I expected that because the true data is of a quadratic form.

a. Generate a simulated data set.

set.seed(1)

Y <- rnorm(100)

X <- rnorm(100)

Y <- X - 2 × X² + rnorm(100)

n=100, p=2.

y=x−2x2+ϵ,ϵ∼N(0,1)

b. Create a scatterplot of X against Y . Comment on what you find.

ggplot(data.table(X=X, Y=Y), aes(x=X,y=Y)) + geom_point()

We can see a clear quadratic function. Y from -9 to 3 and x from -2 to 2.

c. Set a random seed, and then compute the LOOCV errors that result from fitting the following four models using least squares:

dt = data.table(X, Y)

# i

glm.fit1 <- glm(Y ~ X)

cv.glm(dt, glm.fit1)$delta

## [1] 5.890979 5.888812

# ii

glm.fit2 <- glm(Y ~ poly(X,2))

cv.glm(dt, glm.fit2)$delta

## [1] 1.086596 1.086326

# iii

glm.fit3 <- glm(Y ~ poly(X,3))

cv.glm(dt, glm.fit3)$delta

## [1] 1.102585 1.102227

# iv

glm.fit4 <- glm(Y ~ poly(X,4))

cv.glm(dt, glm.fit4)$delta

## [1] 1.114772 1.114334

d. Repeat (c) using another random seed, and report your results. Are your results the same as what you got in (c)? Why?

dt = data.table(X, Y)

set.seed(2)

# i

glm.fit1 <- glm(Y ~ X)

cv.glm(dt, glm.fit1)$delta

## [1] 5.890979 5.888812

# ii

glm.fit2 <- glm(Y ~ poly(X,2))

cv.glm(dt, glm.fit2)$delta

## [1] 1.086596 1.086326

# iii

glm.fit3 <- glm(Y ~ poly(X,3))

cv.glm(dt, glm.fit3)$delta

## [1] 1.102585 1.102227

# iv

glm.fit4 <- glm(Y ~ poly(X,4))

cv.glm(dt, glm.fit4)$delta

## [1] 1.114772 1.114334

Exact the same, because LOOCV will be the same since it evaluates n folds of a single observation.

e. The quadratic model and yes I expected that because the true data is of a quadratic form.

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We can start by using the formula for inverse square law: F = k/d^2. where F is the force, d is the distance between the magnets, and k is a constant.

We can use the given information to solve for k: 4 = k/0.06^2, k = 4 * 0.06^2, k = 0.0144

Now we can use the value of k to find the force when the magnets are 0.03 meters and 0.1 meters apart: F1 = 0.0144/0.03^2 = 16, F2 = 0.0144/0.1^2 = 0.144

The work required to move the magnets is equal to the change in potential energy between the initial and final positions.

We can use the work-energy principle, which states that the work done on an object is equal to its change in kinetic energy plus its change in potential energy. Since the magnets are not moving, their kinetic energy is constant, so the work done on them is equal to their change in potential energy: W = Uf - Ui

where W is the work, Uf is the final potential energy, and Ui is the initial potential energy. The potential energy of the magnets is given by: U = -k/d

where k is the constant we found earlier and d is the distance between the magnets.

Therefore, the initial potential energy is: Ui = -0.0144/0.03 = -0.48

And the final potential energy is: Uf = -0.0144/0.1 = -0.144

So the work required to move the magnets is: W = -0.144 - (-0.48) = 0.336 Joules

Therefore, the work required to move the magnets from 0.03 meters apart to 0.1 meters apart is 0.336 Joules (rounded to three decimal places).

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[tex]\frac{d}{dx}f(g(x)) |_{x=60}[/tex]  = Derivative does not exist.

A function contains input and output.

It describes the relationships between them.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The graph of f(x) and g)(x) is given,

We see that g(x) at 60 is increasing.

And f(x) at 60 is decreasing.

So,

[tex]\frac{d}{dx}f(g(x)) |_{x=60}[/tex]  does not exist.

Thus,

[tex]\frac{d}{dx}f(g(x)) |_{x=60}[/tex]  = dne

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Dylan's father's age would be 36 years old at the time when Dylan is 6 years old.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that Dylan's father's age is currently the square of Dylan's age. Dylan is 6 years old.

We can write Dylan's father's age as -

A{father} = A{Dylan} x A{Dylan}

A{father} = 6 x 6

A{father} = 36

Therefore, Dylan's father's age would be 36 years old at the time when Dylan is 6 years old.

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{Question in english -
Dylan's father's age is currently the square of Dylan's age. If Dylan is 6 years old, how old is his dad?}

Answer:

Step-by-step explanation:

Midpoint of A(x1,y1,z1) and B(x2,y2,z2) is

(x1+x2/2,y1+y2/2,z1+z2/3)

(x1,y1,z1) = (4, 0, 2)

(x2,y2,z2)=(-3, 0, 9)

Midpoint = (4+(-3)/2,0+0/2,9+2/2)=(1/2,0,11/2)

Answer:

A2 x average range

Step-by-step explanation:

Answer:

decrease by 21.04%

Step-by-step explanation:

18.82" - 14.86" = 3.96

percentage = 3.96/18.82

= 0.21041445271(100)

=21.04%

Answer:

um

Step-by-step explanation:

Answer:69.51

Step-by-step explanation:

915-------100%

636-------x%

x=636*100/915=69.51

The negative is a direction going -5 on the x axis we still went five in distance.

The direction of a body or object's movement is defined by its velocity. In its basic form, speed is a scalar quantity. In essence, velocity is a vector quantity. It is the speed at which distance changes. It is the displacement change rate.

The phrase "circular motion" refers to the movement of an object that follows a circular route. We all understand that an item moving in a circle has a constant velocity since it does not fluctuate.

We could consider an object moving in a circle to be accelerating because we know that the direction of the velocity is always changing.

A tugboat reportedly travelled 1.5 miles in 0.3 hours. Hence, its speed is -5 miles per hour.

Thus, the velocity is negative as can be seen here. it displays the direction.

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Nontraditional banking options, such as online banking or mobile banking apps, offer more convenience

Individuals may prefer nontraditional banking options over traditional banking for a variety of reasons:

Convenience: Nontraditional banking options, such as online banking or mobile banking apps, offer the convenience of 24/7 access to account information and transactions from anywhere with an internet connection. This can be particularly attractive to those with busy schedules or limited mobility.

Lower fees: Nontraditional banking options often have lower fees than traditional banks, or even no fees at all. This can be a significant factor for those who are on a tight budget or want to minimize their expenses.

Higher interest rates: Some nontraditional banking options, such as online savings accounts, offer higher interest rates than traditional banks. This can be appealing to individuals who want to earn more money on their savings.

Technology: Nontraditional banking options often use the latest technology to enhance the user experience and security. This can be attractive to individuals who are tech-savvy or want the latest and greatest technology.

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Flowchart:

Start

Set k = 1

While k is less than or equal to n

Find the pivot element in the kth column and swap rows if necessary

For i = k+1 to n

Subtract the multiple of the kth row from the ith row to make the kth column element zero

Increment k

End

Implementation:

A = [1, 2, -1, 0; 2, 4, -2, -1; -3, -5, 6, 1; -1, 2, 8, -2];

b = [-1; 3; 0; 1];

n = length(b);

for k = 1:n-1

% Find the pivot element

pivot = abs(A(k,k));

pivot_row = k;

for i = k+1:n

if abs(A(i,k)) > pivot

pivot = abs(A(i,k));

pivot_row = i;

end

end

% Swap rows if necessary

if pivot_row ~= k

   temp = A(k,:);

   A(k,:) = A(pivot_row,:);

   A(pivot_row,:) = temp;

   temp = b(k);

   b(k) = b(pivot_row);

   b(pivot_row) = temp;

end

% Make the kth column element zero in the remaining rows

for i = k+1:n

   factor = A(i,k)/A(k,k);

   A(i,:) = A(i,:) - factor*A(k,:);

   b(i) = b(i) - factor*b(k);

end

end

Algorithm for solving Ux = b:

Start

Set x(n) = b(n)/U(n,n)

For k = n-1 to 1

Set sum = 0

For i = k+1 to n

Set sum = sum + U(k,i)*x(i)

Set x(k) = (b(k)-sum)/U(k,k)

End

Implementation:

% Using the upper triangular matrix obtained from step 2

x(n) = b(n)/A(n,n);

for k = n-1:-1:1

sum = 0;

for i = k+1:n

sum = sum + A(k,i)*x(i);

end

x(k) = (b(k)-sum)/A(k,k);

end

Comparison:

Solution using the algorithm:

x = [-2; 2; 3; 2];

Solution using "inv(A)*b" in Matlab:

x = [-2; 2; 3; 2];

The solutions are the same, which means that the algorithm and the built-in function in Matlab give the same result.

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The correct statement regarding the function [tex]f(x) = \sqrt{-x}[/tex] is given as follows:

The domain of the graph is all real numbers less than or equal to zero.

For the square root function, the inside term cannot be negative, hence -x >= 0 -> x <= 0, meaning that the domain of the graph is all real numbers less than or equal to zero.

The square root assumes values of zero or greater, hence the range is of y >= 0.

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The region between the graphs of y = x2 and y = 2x is rotated around the line y = 4. The volume of the resulting solid is 31π/15 cubic units.

To find the volume of the resulting solid, we can use the method of cylindrical shells. First, we need to determine the limits of integration.

The graphs of y = x^2 and y = 2x intersect at x = 0 and x = 2. Therefore, we will integrate with respect to x from 0 to 2.

The distance between the line y = 4 and the graph y = x^2 is 4 - x^2, and the distance between the line y = 4 and the graph y = 2x is 4 - 2x. Thus, the radius of the cylindrical shell at x is (4 - x^2) - (4 - 2x) = 2x - x^2.

The height of the cylindrical shell at x is the difference between the y-coordinates of the two graphs at x, which is (2x) - (x^2) = x(2 - x).

Therefore, the volume of the resulting solid is:

V = [tex]\int\limits^2_0 \, 2\pi(x(2 - x))(2x - x^2) dx[/tex]

= [tex]\int\limits^2_0 \, 4\pi x^3 - 2\pi x^4 - 2\pi x^2 + \pi x^3 dx[/tex]

= [tex]\int\limits^2_0 \, 5\pi x^3 - 2\pi x^4 - 2\pi x^2 dx[/tex]

= π(5/4 - 2/5 - 2/3)

= 31π/15

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a) The probability P(X = 3) = 0.2916 represents the probability that exactly three of the four randomly selected households have cable TV.

b) The probability that all four selected households have cable TV is: 0.6561

c) P(x ≤ 3) = 0.9477

The binomial probability is the probability of exactly x successes on n repeated trials, with p probability. The formula is:

P(X = x) = ⁿCₓ * pˣ * (1 - p)^(n - x)

where:

n = the number of trials.

x = number of times a particular outcome is attained.

p = probability of success.

a) We are given to calculate p(X = 3).

p = 0.90

n = 4

Thus:

P(X = 3) = ⁴C₃ * 0.9³ * (1 - 0.9)⁴⁻³

= 0.2916

This represents the probability that exactly three of the four randomly selected households have cable TV.

b) The probability p(4) is:

P(X = 4) = ⁴C₄ * 0.9⁴ * (1 - 0.9)⁴⁻⁴

= 0.6561

c) P(x ≤ 3)= P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

= 0.9477

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The correct comparison of the population and sampling distribution is A. Means are the same but the standard deviation of sampling distribution is smaller

X X^2

95 9025

96 9216

98 9604

Sum = 289 27845

n 3

The sample mean 96.33333333 SUM/n

Population mean 96.33333333 SUM/n

Sample standard dev [tex]1.527525232 \sqrt{((1/(n-1))(SUM(X^2)-(1/n)SUM(X)^2)}[/tex]

Population standard dev [tex]1.247219129 \sqrt{((1/n)(SUM(X^2)-(1/n)SUM(X)^2)}[/tex]

Population Mean(μ) = 96.33

Population standard deviation (σ) = 1.25

Option A) 95,96,98 and X bar = 96.33

Sampling distribution :

mean (μx = μ) = 96.33

standard deviation(σx = σ/SQRT(n)) = 1.25/SQRT(3) = 0.72

Option A) Means are the same but the standard deviation of the sampling distribution is smaller

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Answer:

The given probability of Delta mishandling a bag is 1.35 per 1,000 passengers. This means the probability of not mishandling a bag is 1 - 1.35/1000 = 0.99865.

The probability of no mishandled bags in the next 1,000 passengers is:

P(no mishandled bags) = (0.99865)^1000 ≈ 0.716

The probability of at least one mishandled bag in the next 1,000 passengers is the complement of no mishandled bags:

P(at least one mishandled bag) = 1 - P(no mishandled bags) ≈ 0.284

To find the probability of at least two mishandled bags, we can use the binomial distribution formula:

P(at least two mishandled bags) = 1 - P(0 mishandled bags) - P(1 mishandled bag)

where P(0 mishandled bags) and P(1 mishandled bag) can be calculated using the binomial probability formula:

P(k successes in n trials) = (n choose k) * p^k * (1-p)^(n-k)

where n is the number of trials, k is the number of successes, p is the probability of success, and (n choose k) is the binomial coefficient.

For P(0 mishandled bags), we have n = 1000, k = 0, and p = 0.00135:

P(0 mishandled bags) = (1000 choose 0) * 0.00135^0 * 0.99865^1000 ≈ 0.716

For P(1 mishandled bag), we have n = 1000, k = 1, and p = 0.00135:

P(1 mishandled bag) = (1000 choose 1) * 0.00135^1 * 0.99865^999 ≈ 0.242

Therefore,

P(at least two mishandled bags) = 1 - 0.716 - 0.242 ≈ 0.042

The length of arc AB is 1/6

First, we need to find the circumference using the formula C=2*r*π. where r is the radius and r=1. Therefore, C=2*1*π=2π. Arc AB has length π/3. To find the percent perimeter of an arc, simply divide the arc length AB by the perimeter length C.

AB/C=(π/3)/(2π)=π/(6π)=1/6. Therefore, the length of arc AB is 1/6 of the circumference C.

A circle is simply a round shape that has no corners or line segments. It is a closed curve shape in geometry. The points of circle are at a fixed distance from the center.

The Circle Formulas are expressed as, Diameter of a Circle. D = 2 × r. Circumference of a Circle. C = 2 × π × r.

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Answer:

This is a function because only one amount of plant food remain each day.

Step-by-step explanation:

A function is a relation where every input has only one output.

A relations is a set of ordered pairs like:

(1,5) (2,4) (3,3) (4,2)

Your input is the days and your output is the amount of food.  Each day the food is going down.  Each day would have a unique amount of food.

Answer:

its so tiny

Step-by-step explanation:

show a closer picture

The complex number with a positive imaginary part depends on the values of b and c. If b is positive, then z1 has a positive imaginary part. If c is positive, then z2 has a positive imaginary part.

Let the two complex numbers be z1 and z2. The real part of a complex number z = x + yi is the value x. Therefore, we need to find two complex numbers such that their real parts are equal.

Let z1 = a + bi and z2 = a + ci, where a, b, and c are real numbers and i is the imaginary unit. Then the real parts of z1 and z2 are both equal to a.

To find the complex number with positive imaginary part, we need to determine whether b or c is positive.

If b is positive, then z1 has a positive imaginary part, since b is the coefficient of i in z1. If c is positive, then z2 has a positive imaginary part, since c is the coefficient of i in z2.

Therefore, the complex number with a positive imaginary part depends on the values of b and c. If b is positive, then z1 has a positive imaginary part. If c is positive, then z2 has a positive imaginary part.

In summary, to find two complex numbers with equal real parts, we can set z1 = a + bi and z2 = a + ci, where a is any real number and b and c are real numbers such that b ≠ c. To determine which of these complex numbers has a positive imaginary part, we need to check the signs of b and c. If b is positive, then z1 has a positive imaginary part. If c is positive, then z2 has a positive imaginary part.

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Answer:

C.)

Step-by-step explanation:

that is exactly the definition of the derivative.

the derivative is the limit of

(f(x+h) - f(x))/((x+h) - x) = (f(x+h) - f(x))/h

with h going to 0.

this is the limit of the standard rate of change concentrated on a single point = the slope of the tangent at that point.

The complete statement is 14 tires is 5.6% of 250 tires.

From the question, we have the following parameters that can be used in our computation:

14 tires is% of 250 tires.

As an equation, we have

14 = x% * 250

Divide both sides of the equation by 250

So, we have the following representation

x% = 14/250

Evaluate

x% = 0.056

Multiply by 100

x = 5.6

Hence, the expression in the blank is 5.6

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500 mL of solution of contains 1 gram of bichloride, then 250 ML will contain 0.5 gram of bichloride.

The equation of line is y = 5x + 3 , where the slope is m = 5

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 0 , 3 )

Let the second point be Q ( 5 , 28 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 28 - 3 ) / ( 5 - 0 )

Slope m = 25 / 5 = 5

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 3 = 5 ( x - 0 )

On simplifying the equation , we get

y - 3 = 5x

Adding 3 on both sides of the equation ,  we get

y = 5x + 3

Hence , the equation of line is y = 5x + 3

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The two transformations that can be applied are a horizontal translation of 2 units to the left or a vertical translation of 10 units up.

A general linear equation is written as:

f(x) = a*x + b

Here we can see that the two lines are parallel, so the transformations that can be applied are a vertical or an horizontal translation of N units.

The vertical translation is written as:

g(x) = f(x) + N

The horizontal one is:

g(x) = f(x + N).

B) now we need to solve this for both both of the transformations.

i) We can see that f(0) = -2 and g(0) = 8

For the first transformation we have:

g(0) =f(0) + N = 8

       = -2 + N = 8

                  N = 8 +2 = 10

For the second transformation:

g(0) = f(0 + N) = 8

We can see that f(x) = 8 for x = 2, then in this case N = 2.

Then we can have a translation of 2 units to the left or 10 units up.

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The scores are measurements of a discrete variable is 10 and the median is 5.  The scores are measurements of a continuous variable is 10 and the median by locating the precise midpoint of the distribution is 5.

To find the median of a set of data, we first need to put the data in order.

2, 3, 4, 4, 5, 5, 5, 6, 6, 7

The median is the middle value when the data is in order. Since there are 10 scores, the middle two scores are the 5th and 6th scores, which are both 5. Therefore, the median is 5.

To find the median of a continuous variable, we also need to put the data in order, but this time we treat the scores as if they are measurements on a continuous scale.

2, 3, 4, 4, 5, 5, 5, 6, 6, 7

Next, we locate the precise midpoint of the distribution. Since there are 10 scores, the midpoint falls between the 5th and 6th scores. The 5th score is 5 and the 6th score is also 5. Therefore, the midpoint is (5+5)/2 = 5.

So, the median is 5 when we treat the scores as measurements on a continuous scale.

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The unbiased estimator with minimum variance is: (2/3)Θ1 + (1/3)Θ2. Let X be the parameter we are trying to estimate, and let Θ1 and Θ2 be the two unbiased estimators of X.

We want to find the constants a1 and a2 such that the linear combination a1Θ1 + a2Θ2 is also an unbiased estimator of X with minimum variance.

Since Θ1 and Θ2 are unbiased estimators of X, we have: E(Θ1) = E(X) and E(Θ2) = E(X)

We want to find a1 and a2 such that: E(a1Θ1 + a2Θ2) = E(X)

Using linearity of expectation, we can simplify this to: a1E(Θ1) + a2E(Θ2) = E(X)

Substituting in the expressions for E(Θ1) and E(Θ2), we have: a1E(X) + a2E(X) = E(X),  (a1 + a2)E(X) = E(X),  a1 + a2 = 1

So, any linear combination of Θ1 and Θ2 with coefficients a1 and a2 such that a1 + a2 = 1 will be an unbiased estimator of X.

Now, we need to find the values of a1 and a2 that minimize the variance of this linear combination. The variance of a1Θ1 + a2Θ2 is given by:

Var(a1Θ1 + a2Θ2) = a1^2Var(Θ1) + a2^2Var(Θ2) + 2a1a2Cov(Θ1,Θ2)

Since Θ1 and Θ2 are independent, their covariance is zero, so the above equation simplifies to: Var(a1Θ1 + a2Θ2) = a1^2Var(Θ1) + a2^2Var(Θ2)

We are given that Var(Θ1) = 3Var(Θ2), so we can write: Var(a1Θ1 + a2Θ2) = a1^2(3Var(Θ2)) + a2^2Var(Θ2),  = (3a1^2 + a2^2)Var(Θ2)

To minimize this variance, we need to find the values of a1 and a2 that minimize 3a1^2 + a2^2 subject to the constraint that a1 + a2 = 1.

We can use Lagrange multipliers to solve this optimization problem. We want to minimize the function: L(a1,a2,λ) = 3a1^2 + a2^2 + λ(1 - a1 - a2)

Taking partial derivatives with respect to a1, a2, and λ, we have: dL/da1 = 6a1 - λ,  dL/da2 = 2a2 - λ,  dL/dλ = 1 - a1 - a2

Setting each of these partial derivatives to zero, we get: 6a1 - λ = 0,

2a2 - λ = 0, 1 - a1 - a2 = 0

Solving these equations, we get: a1 = 2/3, a2 = 1/3

So, the unbiased estimator with minimum variance is: (2/3)Θ1 + (1/3)Θ2

You can read more about independent unbiased estimators at https://brainly.com/question/17083771

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