They both have the same confidence coefficient of 1/2, meaning that they both have a 50% chance of containing the true parameter value. Ultimately, the choice between the two intervals would depend on the specific goals of the analysis and the trade-offs between precision and coverage.
(a) We have that X ~ Beta(θ,1) and Y = -(log X)^-1. We need to find the confidence coefficient of the set [Y/2, Y]. Since Y is a transformation of X, we can use the transformation theorem to find the distribution of Y:
Let g(x) = -(log x)^-1. Then g'(x) = (1/x)(log(x)^-2), and so by the transformation theorem, we have that Y ~ Beta(1,θ).
Now we can use the properties of the Beta distribution to find the confidence coefficient of [Y/2, Y]:
P(Y/2 ≤ Y ≤ Y) = P(1/2 ≤ X ≤ 1) = Beta(θ,1)(1) - Beta(θ,1)(1/2) = 1/2.
Therefore, the confidence coefficient of [Y/2, Y] is 1/2.
(b) To find a pivotal quantity, we can use the fact that if X ~ Beta(θ,1), then X/(1-X) ~ Beta(θ,1). Let Z = X/(1-X). Then we have:Z ~ Beta(θ,1)
log(Z) ~ log(Beta(θ,1))
log(Z) ~ Σ(log(X[i])) - (n+1)log(1-X[i])
Since Z is a pivotal quantity, we can use it to construct a confidence interval with the same confidence coefficient as [Y/2, Y]. We have:
P(Y/2 ≤ Y ≤ Y) = P(log(Y) ≥ -2log(2)) - P(log(Y) > -log(2))
= P(log(Z) ≤ 2log(2)) - P(log(Z) > log(2))
= 1 - 2B(θ,1)(2^(-2)) - B(θ,1)(2^(-1))
Therefore, a confidence interval with the same confidence coefficient as [Y/2, Y] is given by:[exp(-2log(2)), exp(-log(2))] = [1/4, 1/2]
(c) Comparing the two confidence intervals, we can see that they have different widths. The interval [Y/2, Y] has a width of Y/2, while the interval [1/4, 1/2] has a width of 1/4. The interval [Y/2, Y] is centered around Y, while the interval [1/4, 1/2] is centered around 3/8. Therefore, the two intervals provide different information about the location and spread of the distribution.
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AVALIAÇÃO DIAGNÓSTICA
Resolva os problemas abaixo
1) O quilo do feijão que custava R$ 3,90 teve um aumento de 70% Oual é o novo preço do quilo do
feijão?
2) O aluguel de uma casa teve um reajuste e passou de R$ 500,00 para R$ 925,00. Qual foi o percentual
de aumento do aluguel dessa casa
Answer:
hhhsyeuru isuegrjro ehgeurov didyrhy
Steven sold his old car and deposited the $3500 in a savings account at 3.5 percent interest for 2.5 years.
What was the total amount of money in the account at the end of this time?
Answer:
3500.035
I'm not sure
.
Step-by-step explanation:
.
Answer: It’s $3,806.25
Step-by-step explanation:
No explanation, I did the quiz and the other person who answered gave an answer that wasn’t in the multiple answers so I guessed and got it correct.
Which ordered pair is in the solution set of the inequality shown?
Answer:
number 2: (-6, 0)
The space that sand fills varies directly with its mass. If 2,400 kg of sand fill 1.5 cubic meters, how much sand is needed to fill 2.25 cubic meters? PLEASE I REALLY NEED HELP!
Answer:
3,600 kg
Step-by-step explanation:
2,400÷6=400
400×3=1200
2,400+1,200= 3,600 kg
What is the value of so that −10and 10are both solutions of 2−=70
Answer:I think 7
Step-by-step explanation:
Angela can paint 3 sections in 25 minutes.
How many minutes will it take Angela to
paint 12 sections?
Answer:
Análisis del problema
Nos dan como datos el tiempo que se tarda cada uno en pintar la habitación:
Gerardo: 3 horas
Ángel: 6 horas
La velocidad de trabajo podemos definirla como dada por la cantidad de habitaciones que pueden pintar sobre el tiempo: H/t
Gerardo: 1 hab /3h
Ángel: 1 hab / 6h
Sumamos ambas velocidades de trabajo:
Por lo tanto entre los dos pintarían una habitación en dos horas.
5x + 2y = 10
What is the substitution?
Hi there!
The substitutions are 10 and 0.
Answer the photo below thanks
Answer:
x=50
Step-by-step explanation:
65+65=130
180-130=50
Answer:
50 is the answer
Step-by-step explanation:
this is a isosceles triangle having 65 and 65
then 65 + 65 + x = 180 property of traingle
130 + x = 180
x = 180- 130 = 50
the sum of 8 and B is greater than 22
Given:
The sum of 8 and B is greater than 22.
To find:
The inequality for the given statement and its solution.
Solution:
We know that, sum of two number is the addition of two numbers.
Sum of 8 and B = 8+B
It is given that, the sum of 8 and B is greater than 22.
[tex]8+B>22[/tex]
Subtracting 8 from both sides, we get
[tex]8+B-8>22-8[/tex]
[tex]B>14[/tex]
Therefore, the required inequality for the given statement is [tex]8+B>22[/tex] and the solution is [tex]B>14[/tex].
I know the answer for this isn't a , but I'm not sure what the answer is. Cuz I would think you would be z y , y x, and XZ but that's not answer choice
Answer:
its the first one
Step-by-step explanation:
The student council was preparing for the wellness sale. The members divided each type of the donated items equally onto plates. Each plate contained only 1 type of item and every plate had exactly the same number of items. There were no leftovers. What is the greatest number of items that could have been placed on each plate? Wellness Sale Donations Celery 63 Cucumbers 14 Carrots 35 The greatest number of items that each plate could have is nothing items. (Type a whole number.)
Answer:
The greatest number of items on each plate is 7
Step-by-step explanation:
Given
[tex]Celery = 63[/tex]
[tex]Cucumber = 14[/tex]
[tex]Carrot = 35[/tex]
Required
Determine the greatest number of items on each plate
To do this, we simply calculate the GCF of 63, 14 and 35
[tex]63 =3 * 3 * 7[/tex]
[tex]14 = 2 * 7[/tex]
[tex]35 = 5* 7[/tex]
The GCF is:
[tex]GCF = 7[/tex]
Hence:
The greatest number of items on each plate is 7
The Students' Conjectures Emily and Zach have two different polynomials to multiply: Polynomial product A: (4x2 – 4x)(x2 – 4) Polynomial product B: (x2 + x – 2)(4x2 – 8x)
Complete Question:
Emily and Zach have two different polynomials to multiply: Polynomial product A: (4x2 – 4x)(x2 – 4) Polynomial product B: (x2 + x – 2)(4x2 – 8x) They are trying to determine if the products of the two polynomials are the same. But they disagree about how to solve this problem.
Answer:
[tex]A = B[/tex]
Step-by-step explanation:
See comment for complete question
Given
[tex]A: (4x^2 - 4x)(x^2 - 4)[/tex]
[tex]B: (x^2 + x - 2)(4x^2 - 8x)[/tex]
Required
Determine how they can show if the products are the same or not
To do this, we simply factorize each polynomial
For, Polynomial A: We have:
[tex]A: (4x^2 - 4x)(x^2 - 4)[/tex]
Factor out 4x
[tex]A: 4x(x - 1)(x^2 - 4)[/tex]
Apply difference of two squares on x^2 - 4
[tex]A: 4x(x - 1)(x - 2)(x+2)[/tex]
For, Polynomial B: We have:
[tex]B: (x^2 + x - 2)(4x^2 - 8x)[/tex]
Expand x^2 + x - 2
[tex]B:(x^2 + 2x - x - 2)(4x^2- 8x)[/tex]
Factorize:
[tex]B:(x(x + 2) -1(x + 2))(4x^2- 8x)[/tex]
Factor out x + 2
[tex]B:(x -1) (x + 2)(4x^2- 8x)[/tex]
Factor out 4x
[tex]B:(x -1) (x + 2)4x(x- 2)[/tex]
Rearrange
[tex]B: 4x(x - 1)(x - 2)(x+2)[/tex]
The simplified expressions are:
[tex]A: 4x(x - 1)(x - 2)(x+2)[/tex] and
[tex]B: 4x(x - 1)(x - 2)(x+2)[/tex]
Hence, both polynomials are equal
[tex]A = B[/tex]
In rectangle PQRS, SP = 3 and RS = 4. What is the length of PR? (Hint: use
the Pythagorean theorem to solve for the diagonal) *
Consider the function f(x) =2x+3 Find the average rate of change from the following points x=2 and x= 6
Step-by-step explanation:
step 1. m = 2.
step 2. for a linear equation the average rate of change between any points is the slope m.
What is an equation of the line that passes through the points (2, -2) and (8,4)?
Please I’ll give you BRAINLEST
Answer:
y=x-4
Step-by-step explanation:
m=(y2-y1)/(x2-x1)=(4-(-2))/(8-2)=(4+2)/6=6/6=1
slope is 1
y-y1=m(x-x1) where m=slope
y-(-2)=1(x-2)
y+2=x-2
y=x-2-2
y=x-4
Find the solution of y = 5x – 4 for x = –6.
(26, –6)
(-6, -[tex]\frac{2}{5}[/tex])
(–6, –50)
(–6, –34)
R950 is divided between Ann, Jill, Agnes Ann gets R100 more than Jill, Jill gets R50 more than Agnes. How much did Agnes get
I need help on this one math problem
Answer:
B
I hope this helps.....
Triangle D E F is shown. Angle D E F is a right angle. The length of hypotenuse DF is 13, the length of E F is 5, and the length of E D is 12.
What is the length of the side opposite ∠D?
units
sin(D) =
Answer:
5 and 5/13
Step-by-step explanation:
What is the length of the side opposite ∠D?
✔ 5
units
sin(D) =
✔ 5/13
What is the prime factorization of 91?
Answer:
The factors of 91 by prime factorization are 1, 7, 13 and 91. Here, 7, and 13 are the prime factors of 91.
Step-by-step explanation:
What number should be added to both sides of the equation to complete the square?
x^2-10x=12
Answer:
Step-by-step explanation:
x²-10x = 12
Coefficient of the x term: -10
Divide in half: -5
Square it: (-5)² = 5²
Add 5² to both sides:
x²-10x+5² = 12+5²
(x-5)² = 37
Write −(1/4⋅1/4⋅1/4⋅1/4) using exponents.
Answer:
-(1/4)^4
Step-by-step explanation:
Hope it helped!!!
Please help quick will give brainliest!
Answer:
The function's behavior close to the vertical asymptote, x = 2 is;
[tex]\lim\limits_{x \to 2^-} f(x) = \infty[/tex] and [tex]\lim\limits_{x \to 2^+} f(x) = -\infty[/tex]
Step-by-step explanation:
From the graph of the function. we have;
1) As 'x' approaches 2 from the left (x → 2⁻), the graph with 'u' shape located in the middle of the three graphs, approaches infinity (arrow pointing up)
2) As 'x' approaches 2 from the right (x → 2⁺), the graph with 'n' shape located at the right side of the three graphs, approaches negative infinity (-∞) (arrow pointing down)
Therefore, the function's behavior close to the vertical asymptote, x = 2 is given as follows;
[tex]\lim\limits_{x \to 2^-} f(x) = \infty[/tex] and [tex]\lim\limits_{x \to 2^+} f(x) = -\infty[/tex]
How many pounds are equal to 400 ounces
Answer: 25 pounds
Step-by-step explanation:
1 pound = 16 oz
400 oz / 16 oz = 25 pounds
I am not a professional, I am simply using prior knowledge!
Note- It would mean the world to me if you could mark me brainliest!
what is the inequality of -5x + 19 ≥ 9
Answer:
x<=2
Step-by-step explanation:
-5x+19>=9
-5x>=9-19
-5x>=-10
5x>=10
x>=10/5
x>=2
x<=2
any help would be cool
Step-by-step explanation:
the shape has been split into 2 shapes. one cuboid and a triangular prism . work out the volume of each shape .
hint : volume : h×l×w ( height times length times width)
so the cubiod is 12 times 29 times 12 =
you work out the answer for that .
the triangular prism you try working out the volume.
What is the operation used in 3r?
-subtraction
-addition
-multiplication
-division
Answer:
Multiplication
Step-by-step explanation:
3r means 3 times R. We don't write it just like we don't write 1.0 for 1 or 1.000... A number in front of a variable means that number times that variable.
Hope this helps! <3
if a dozen eggs cost $3.84 calculate the cost of 30 eggs
Answer:
30
Step-by-step explanation:
what is the measure of EGF?
Answer:
i think c
Step-by-step explanation:
Answer:
B) 40.18°
Step-by-step explanation:
since it's a right triangle and you know values for opposite and hypotenuse you can use:
sin x = 12/18.6
this comes out to be 40.18°
Compounds A and B are used in an experiment.
The equation y=700(0.8)x represents the remaining amount of compound A, in grams, after x hours. The table shows the remaining amount of compound B.
Time (h) Grams of B
1 800
2 400
3 200
What is the positive difference in the initial amount of each compound?
Enter your answer in the box.
9514 1404 393
Answer:
900 grams
Step-by-step explanation:
The equation tells you the initial amount of A is 700 grams.
The table tells you B is being cut in half each hour, so the amount when h=0 is 2×800 = 1600 grams.
The difference in the initial amounts is ...
1600 -700 = 900 . . . grams