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faust18 [17]
3 years ago
15

Two surveys were independently conducted to estimate a population mean, μ. denote the estimates and their standard errors by x1

and x2 and σx1 and σx2 . assume that x1 and x2 are unbiased. for some α and β, the two estimates can be combined to give a better estimator:
Mathematics
1 answer:
lyudmila [28]3 years ago
3 0

Hi there what you need is lagrange multipliers for constrained minimisation. It works like this,

V(X)=α2σ2X¯1+β2\sigma2X¯2

Now we want to minimise this subject to α+β=1 or α−β−1=0.

We proceed by writing a function of alpha and beta (the paramters you want to change to minimse the variance of X, but we also introduce another parameter that multiplies the sum to zero constraint. Thus we want to minimise

f(α,β,λ)=α2σ2X¯1+β2σ2X¯2+λ(\alpha−β−1).

We partially differentiate this function w.r.t each parameter and set each partial derivative equal to zero. This gives;

∂f∂α=2ασ2X¯1+λ=0

∂f∂β=2βσ2X¯2+λ=0

∂f∂λ=α+β−1=0

Setting the first two partial derivatives equal we get

α=βσ2X¯2σ2X¯1

Substituting 1−α into this expression for beta and re-arranging for alpha gives the result for alpha. Repeating the same steps but isolating beta gives the beta result.

Lagrange multipliers and constrained minimisation crop up often in stats problems. I hope this helps!And gosh that was a lot to type!xd

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Jen’s goal is to run a total of 22 miles in five days. The table below shows her log for the number of miles she ran on Monday,
Ronch [10]

Answer: 5.875 miles run on Friday to reach her goal by Jen

Step-by-step explanation:

Since we have given that

Part of distance covered on Monday by Jen is given by

4\frac{3}{4}=\frac{19}{4}

Part of distance covered on Tuesday by Jen is given by

5\frac{1}{8}\\\\=\frac{41}{8}

Part of distance covered on Wednesday by Jen is given by

0

Part of distance covered on Thursday by Jen is given by

6\frac{1}{4}\\\\=\frac{25}{4}

Total part of distance covered in these four days by Jen is given by

\frac{19}{4}+\frac{41}{8}+0+\frac{25}{4}\\\\=\frac{38+41+0+50}{8}\\\\=\frac{129}{8}=16.125\ miles

Remaining part of distance will be covered on Friday to reach her goal which is given by

22-16.125=5.875\ miles

Hence, 5.875 miles run on Friday to reach her goal by Jen.


5 0
3 years ago
Read 2 more answers
Function f is shown on the graph below where two points are marked. If function f is horizontally compressed by a factor of 2, p
lilavasa [31]

Answer:

If you have    

f(x) = x^2

The point  (2,4)   would be transformed to (1,1)

Step-by-step explanation:

If your compression is horizontal then the transformation you are making is the following

g(x)  = f(x/2)

Therefore, if you have    

f(x) = x^2

The point  (2,4)   would be transformed to (1,1)

5 0
3 years ago
Please help!! For each sum or product, determine whether the result is a rational number or an irrational number. Then choose th
Troyanec [42]
1. Rational/The sum of two rationals is always rational
2. Irrational/ the sum of a rational and an irrational is always irrational
3. Irrational/The product of a nonzero rational and an irrational is always irrational
4. Rational/The product of two rationals is always rational

Pretty much all the irrational numbers are the ones with radical signs over them and the rational numbers are the fractions and whole numbers. Once you identify the two numbers to be rational or irrational, you can then find your answer within the second part of the answers. 
4 0
3 years ago
Find the solutions to 9x^2-54x=0
astra-53 [7]

Answer:

x₁ = 0

x₂ = 6

Step-by-step explanation:

9x² - 54x = 0

9x(x - 6) = 0

x(x - 6) = 0

x = 0

x - 6 = 0 → x = 6

Hope this helps! :)

7 0
3 years ago
Read 2 more answers
Y=0.2(4)x is it exponential growth or decay
Dmitry [639]

Answer:

growth

Step-by-step explanation:

This is of the form

y = ab^x  where a is the initial value and b is either growth or decay

if b > 1 then it is growth

b <1 it is decay

a = .2

b = 4

Since b>1 it is growth

5 0
3 years ago
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