Suppose that Y1, Y2, ..., Yn are random variables with exponential distribution of parameter θ. find
a confidence interval of 100(1 − a) % for t(θ) = θ2.
Note: Keep in mind that the MLS for the mean of the exponential distribution is given by:=Y.Use
the probability of invariance to find MLS of the variance
Answers
To construct a confidence interval for t(θ) = θ², the MLE for the variance is (Y)². The confidence interval is given by (Y² - Z * sqrt((Y²)²/n), Y² + Z * sqrt((Y²)²/n)).
To find a confidence interval for t(θ) = θ², where Y1, Y2, ..., Yn are random variables with an exponential distribution of parameter θ, we can use the method of maximum likelihood estimation (MLE) and the probability of invariance.
First, we find the MLE for the mean of the exponential distribution, which is Y, the sample mean. Next, we apply the probability of invariance to find the MLE for the variance. The variance of an exponential distribution is equal to the square of its mean, so the MLE for the variance is (Y)².
Now, we can construct a confidence interval for t(θ) = θ² using the asymptotic normality of the MLE. The MLE Y follows an asymptotic normal distribution with mean θ and variance θ²/n, where n is the sample size.
Based on this, the confidence interval is given by:
CI = ( (Y)² - Z * sqrt(((Y)²)²/n), (Y)² + Z * sqrt(((Y)²)²/n) ),
where CI is the confidence interval, Z is the critical value from the standard normal distribution corresponding to the desired confidence level (1-a), Y is the sample mean, and n is the sample size.
So, the confidence interval for t(θ) = θ² is given by the above expression.
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Related Questions
3 3/5 into decimal. (with detailed explanation) - (mixed fraction)
Answers
Answer:
3.6
Step-by-step explanation:
3 3/5 into decimal.
First, look at 3/5. 3 divided by 5 equals 0.6.
Next, add the 3 to the 0.6 to get: 3.06
Candy draws a square design with a side length of x inches for the window at the pet shop. She takes the design to the printer and asks for a sign that has an area of 16x2 – 40x + 25 square inches. A square labeled 16 x squared minus 40 x + 25 What is the side length, in inches, of the pet shop sign?
Answers
Answer:
length of side of square = (4x - 5) inches
Step-by-step explanation:
We are given;
Area of square = 16x² – 40x + 25
Let's find the roots of this quadratic equation [-b ± √(b² - 4ac)]/2a
Thus;
x = [-(-40) ± √((-40)² - 4(16 × 25)]/(2×16)
x = [40 ± √(1600 - 1600)]/32
x = (40 ± 0)/32
x = 40/32
x = 5/4
Thus, the factors of the polynomial are;
(4x - 5)²
So,
Area = 16x² – 40x + 25 = (4x - 5)²
Since, the right hand side is (4x - 5)² and area of square is (length of side)², thus we can say that length of side of square is (4x - 5) inches
show your working please.
Answers
Offer B is the best value for money because each kg cost is £0.61 and in offer 'A' each kg cost is £0.7.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
We have:
2 bags for £35
2 bags means 50 kg (2×25)
Each kg cost = 35/50 = £0.7 per kg
3 bags for £92.50
3 bags means 150 kg
Each kg cost = 92.50/150 = £0.61 per kg
As we can see, offer B has a low cost per kg
Thus, offer B is the best value for money because each kg cost is £0.61 and in offer 'A' each kg cost is £0.7.
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Help I do t no and I have a big test today
Answers
Answer:
the area of the trapezoid is 78cm^3
Step-by-step explanation:
How do i do this question? Please help...
Answers
y = -2x + 2
slope = -2
perpendicular slope = 1/2 (-ve inverse of the slope)
coordinates (0, 1)
y - y1 = m(x -x1)
y - 1 = 1/2(x - 0)
y = 1/2x + 1
which is the graph of linear inequality x-2y>-12
Answers
Answer:
y> -6 -1/2x
Step-by-step explanation:
Well to graph it we have to first put it in propper form.
So to get x on the other side we do -x to the other side so now we have 2y > -x -12.
So now to get y by itself we divide everything by 2.
So y> -6 -1/2x.
Answer:
y> -6 -1/2x
Step-by-step explanation:
does tan^2x = sin^2x/cos^2x
Answers
Answer:
Yes they both are equal
Adult tickets to a basketball game cost $5. Student tickets cost $1. A total of $2,791 was collected on the sale of 1,275 tickets. How many of each type of ticket were sold?
Answers
9514 1404 393
Answer:
379 adult tickets896 student ticketsStep-by-step explanation:
Let 'a' represent the number of adult tickets sold. Then (1275-a) is the number of student tickets sold. The total revenue was ...
5a +1(1275 -a) = 2791
4a = 1516 . . . subtract 1275 and simplify
a = 379 . . . . . divide by 4
1275-a = 896
379 adult and 896 student tickets were sold.
john walks to move from Point A to Point B. To avoid the pond, he must walk 36 meters south and 49 meters east. However, he wants to go through the pond in order to save time. To the nearest meter, calculate how many meters would be saved if john rows a boat across the pond
Answers
The distance John would have to walk to get from point A to point B without going through the pond is 60.84 meters.
Since, John walks 36 m south and 49 m east which covered the distance equal to the hypotenuse of a right triangle
Using the Pythagorean theorem
c² = a² + b²
c² = 36² + 49²
c² = 1296 + 2401
c² = 3697
c = √3697
c = 60.84 m
Thus, the distance is 60.84 meters.
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in still water , your small boat averages 8 miles per hour. it takes you the same amount of time to travel 15 miles downstream , with the current , as 9 miles upstream , against the current. what is the rate of the water's current?
Answers
Answer:
in still water, a boat averages 8 miles per hour. It takes the same amount of time to travel 30 miles downstream, with the current, as 18 miles upstream, against the current. What is the rate of the water's current.
Step-by-step explanation:
Let c=speed of current in mph
c+8=speed of boat downstream in mph
c-8=speed of boat upstream in mph
Travel time= distance/speed
30/8+c=18/8-c
240-30c=144+18c
48c=96
c=2 mph
ans
rate of water's current = 2 mph
on April 10 a woman obtains a loan from her bank to be repaid on June 29. If the bank's discount rate is 13
2
2
1
%
, what must be the face value of a non-interest-bearing note that will have proceeds of $485 ? (\$500.00) 6. On July 10 a man needs $2350, which he plans to repay on September 18. He gets a loan from a bank that has a bank discount rate of 14.4%. What will be the face value of the noninterest-bearing note that he signs?
Answers
The face value of the non-interest-bearing note for the woman's loan should be approximately $500.26. The face value of the non-interest-bearing note for the man's loan should be approximately $2417.91.
To find the face value of a non-interest-bearing note, we can use the formula:
Face Value = Proceeds / (1 - Discount Rate * (Days to Maturity / 360))
1. Calculation for the woman's loan:
Proceeds = $485
Discount Rate = 13.22%
Days to Maturity = 80 (from April 10 to June 29)
Face Value = $485 / (1 - 0.1322 * (80 / 360))
Face Value = $485 / (1 - 0.1322 * 0.2222)
Face Value = $485 / (1 - 0.0294)
Face Value = $485 / 0.9706
Face Value = $500.26 (approximately)
Therefore, the face value of the non-interest-bearing note for the woman's loan should be approximately $500.26.
2. Calculation for the man's loan:
Amount needed = $2350
Discount Rate = 14.4%
Days to Maturity = 70 (from July 10 to September 18)
Face Value = $2350 / (1 - 0.144 * (70 / 360))
Face Value = $2350 / (1 - 0.144 * 0.1944)
Face Value = $2350 / (1 - 0.0279)
Face Value = $2350 / 0.9721
Face Value = $2417.91 (approximately)
Therefore, the face value of the non-interest-bearing note for the man's loan should be approximately $2417.91.
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Annabella spends $2.25 per gallon on gas at the gas station. After driving a certain distance, she stops at a second gas station and spends $2.15 per gallon on gasoline.Annabella can express her average cost per gallon of gasoline as 2.25 x 2.15(x 5)2x 5.What is the meaning of the parts of this rational expression in the context of the situation
Answers
(2x + 5)² in the denominator represents the total number of gallons of gas purchased in the whole trip squared.
Annabella spends $2.25 per gallon on gas at the gas station. After driving a certain distance, she stops at a second gas station and spends $2.15 per gallon on gasoline.
Annabella can express her average cost per gallon of gasoline as 2.25 × 2.15(x + 5)/(2x + 5)²
The meaning of the parts of this rational expression in the context of the situation are as follows: 2.25 and 2.15 are the cost per gallon of gas at the two different gas stations.
x represents the number of gallons of gas bought at the first station.
5 is the number of miles driven between the first and second gas stations. And 2x + 5 is the total number of gallons of gas used in the entire trip (from the first gas station to the second).
Therefore, (x + 5) is the amount of gasoline bought from the second gas station, and 2x is the amount of gasoline bought from the first gas station.
The expression (x + 5)/(2x + 5) represents the weighted average of the cost per gallon of gas at the two gas stations.
Finally, (2x + 5)² in the denominator represents the total number of gallons of gas purchased in the whole trip squared.
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gym lockers are numbered from 1 to 99 using metal digits glued onto each locker. how many 3s are needed?
Answers
The number of times the digit '3' is needed to label the gym lockers numbered from 1 to 99 is 20 times.
We can analyze the pattern of numbers from 1 to 99 to determine the frequency of the digit '3'.
From 1 to 9, there is only one number that contains the digit '3', which is 3 itself.
Therefore, there is one occurrence of '3' in this range.
From 10 to 19, there are ten numbers, and only one of them, 13, contains the digit '3'.
From 20 to 29, there is only one number that contains the digit '3', which is 23.
From 30 to 39, there are ten numbers, and each one of them contains the digit '3'.
Following this pattern, we can see that the digit '3' appears 20 times between 1 and 99.
Hence, we need the digit '3' a total of 20 times to label all the gym lockers numbered from 1 to 99.
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Jack's house is located at the point (-2, 3) and Jill's house is located at the point (4, -5). They plan to meet up at the hill located halfway between there two houses what is the coordinate location of the Hill
Answers
The coordinate location of the hill halfway between them is (1, -1).
How to find the distance between two points?Jack's house is located at the point (-2, 3) and Jill's house is located at the point (4, -5). They plan to meet up at the hill located halfway between there two houses.
The coordinate location of the hill can be calculated as follows:
using mid point formula,
(x, y) = (x₁ + x₂ / 2, y₁ + y₂ / 2)
using the end points (-2, 3) and (4, -5)
(x, y) = (-2 + 4 / 2, 3 - 5 / 2)
(x, y) = (2 / 2. -2 / 2)
(x, y) = (1, -1)
Therefore, the coordinate location of the hill is (1, -1).
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Which Function is equivalent to g(x) = x2 + 7x - 18?
A) g(x) = (x-9) (x+2)
B) g(x) = (x+9) (x-2)
=
C) g(x) = (x+6) (x-3)
D) g(x) = (x-6) (x+3)
Answers
Answer:
the answer is b
Step-by-step explanation:
help this works
The function g(x) = x² + 7x - 18 is equivalent to the function g(x) = (x + 9)(x - 2). Then the correct option is B.
What is factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The function is given below.
g(x) = x² + 7x - 18
Factorize the function, then we have
g(x) = x² + 7x - 18
g(x) = x² + 9x - 2x - 18
g(x) = x (x + 9) - 2(x + 9)
g(x) = (x + 9)(x - 2)
The function g(x) = x² + 7x - 18 is equivalent to the function g(x) = (x + 9)(x - 2). Then the correct option is B.
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HELP ME PLEASE AND QUICK IM CRYINGGGG At the We-Pack Shipping, the workers can unload 28 trucks in 7 hours. Which of the following is a correct unit rate for this situation? (4 points)
a
1 truck per hour
b
4 hours per truck
c
1 over 4 of a truck per hour
d
1 over 4 of an hour per truck
Answers
Answer:
D
Step-by-step explanation:
1 over 4 of an hour per truck
Find a basis for the null space of the matrix
⎣
⎡
1
−2
0
0
1
2
−5
6
−8
1
−2
1
4
−2
9
⎦
⎤
Answers
Basis for null space: [2, -2, 1]. This vector, along with its scalar multiples, forms a basis for the null space of the given matrix.
To find a basis for the null space of the matrix:
\[
\begin{bmatrix}
1 & -2 & 0 \\
0 & 1 & 2 \\
-5 & 6 & -8 \\
1 & -2 & 1 \\
4 & -2 & 9 \\
\end{bmatrix}
\]
we need to solve the homogeneous equation \(Ax = 0\), where \(A\) is the given matrix and \(x\) is a vector.
Performing row reduction or Gaussian elimination on the augmented matrix \([A | 0]\), we obtain the row-echelon form:
\[
\begin{bmatrix}
1 & 0 & -2 \\
0 & 1 & 2 \\
0 & 0 & 0 \\
0 & 0 & 0 \\
0 & 0 & 0 \\
\end{bmatrix}
\]
This indicates that the equation \(x_1 - 2x_3 = 0\) and \(x_2 + 2x_3 = 0\). Choosing \(x_3\) as a free variable, we can express the solution as \(x = [2x_3, -2x_3, x_3]\).
Therefore, a basis for the null space consists of the vector \([2, -2, 1]\) or any scalar multiples of it.
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Question : Find a basis for the null space of the matrix
\[
\begin{bmatrix}
1 & -2 & 0 \\
0 & 1 & 2 \\
-5 & 6 & -8 \\
1 & -2 & 1 \\
4 & -2 & 9 \\
\end{bmatrix}
\]
find the sum of the first 50 terms -6, -2, 2, 6,…
Answers
Answer:
4600
Step-by-step explanation:
witch product is less than
\( \frac{5}{8} \)
Answers
Answer:
Everything that is lower than 5/8.Step-by-step explanation:
It's pretty obvious.
You need to add 2 fractions up.
If it's lower than 5/8, then you are correct.
2
How much water will a cone hold that has a diameter of 6 inches and a height of 21 inches.
Use 3. 14 for 7 and round your answer to the nearest whole number.
A 66 cubic inches
B 198 cubic inches
C) 594 cubic inches
D 2374 cubic inches
Answers
The volume of water a cone with a diameter of 6 inches and a height of 21 inches can hold is 198 cubic inches. So, the correct answer is B) 198 cubic inches.
To find the volume of water a cone with a diameter of 6 inches and a height of 21 inches can hold, we will use the formula for the volume of a cone: V = (1/3)πr²h.
Given a diameter of 6 inches, the radius (r) is 3 inches. The height (h) is 21 inches, and we will use 3.14 as an approximation for π.
V = (1/3) * 3.14 * (3²) * 21
V = (1/3) * 3.14 * 9 * 21
V = 3.14 * 3 * 21
V = 197.82 cubic inches
Rounding to the nearest whole number, the volume of water the cone can hold is approximately 198 cubic inches. Therefore, the answer is B) 198 cubic inches.
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The width of a rectangle is 5 feet less than the length. The perimeter is 62. Find the length and width of the rectangle.
Variables: ___________________________
Model equation: ______________________________
Length of the rectangle: ______________________________
Width of the rectangle: ______________________________
Answers
Perimeter formula: p = 2(w + l)
The perimeter is 62.
p = 62
The width of a rectangle is 5 feet less than the length.
w = l - 5
Substitute and solve.
62 = 2[(l - 5) + l)]
62 = 2l + 2l - 10
62 = 4l - 10
72 = 4l
18 = l
Substitute and solve for the width
w = 18 - 5
w = 13
Therefore, the length is 18 and the width is 13.
Best of Luck!
Answer:
see below and attached.
Step-by-step explanation:
Perimeter (P) = 2 L (Length) + 2 W (Width)
where P = 62
W = L - 5
P = 2L + 2W
62 = 2L + 2(L -5)
62 = 2L + 2L - 10
72 = 4L
L = 72/4
L = 18
W = L - 5
W = 18 - 5
W = 15
Variables : P, L, W
Model equation: P = 2L + 2W
Length of the rectangle: 18
Width of the rectangle: 13
Find the value of g (7) for the function below.
Answers
Answer:
B. 45/8
Step-by-step explanation:
\(g(7)=\frac{7}{8}(7)-\frac{1}{2}\)
\(g(7)=\frac{49-4}{8}\)
\(g(7)=\frac{45}{8}\)
A. Find the indicated number of geometric mean/s between the given two numbers.
1. 5 and 20 [ 1 term ]
2. 8 and 512 [2 terms]
3. 2 and 50 [ 1 term ]
4. 6 and 486 [3 terms]
5. 4 and 108 [2 terms]
Answers
9514 1404 393
Answer:
see attached
Step-by-step explanation:
The ratio of the given terms is the common ratio raised to a power equal to the number of means plus 1.
1)For example, the common ratio in the sequence 5, __, 20 will be r, where ...
r^2 = 20/5 = 4 ⇒ r = 4^(1/2) = 2
Then the mean is found by multiplying 5 by this ratio: 5×2 = 10.
__
2-5)The same method is used for finding the common ratio and then the intermediate means. Each mean is the previous term multiplied by the common ratio. Results are summarized in the attached table.
_____
Additional comment
When there are a number of similar calculations to be done, it is convenient to let a spreadsheet do them.
![A. Find the indicated number of geometric mean/s between the given two numbers.1. 5 and 20 [ 1 term ]2.](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/YeJCbPqFtVuUKkjzfYWwrhYlPRMDf3JT.png)
O A. All real numbers
O B. y> 0
O c. y> 4
O D. y>4
Answers
Answer:
A
Step-by-step explanation:
cause an exponent and be any number
If Joe has a package of 25 cookies, and he eats 15 of them, what percent of the
package did Joe eat? *
Y pur answer
Answers
Answer:
60%
Step-by-step explanation:
15/25=60%
you ate 15 out of 25 so that means you ate 3 out of 5 if you divide both 15 and 25 by 5. And 3 out of 5 is 60%.
Claire correctly solved the proportion StartFraction x over 4 EndFraction = StartFraction 36 over 16 EndFraction for x by using cross products to get the equation 16 x = 144 and then dividing both sides by 16 to get x = 9. She showed that she can use cross products to solve the proportion because she gets the same answer if the solves it as shown.What property allowed her to go from StartFraction x over 4 EndFraction = StartFraction 36 over 16 EndFraction to StartFraction x over 4 EndFraction times 4 = StartFraction 36 over 16 EndFraction times 4?
Answers
Answer:
Multiplication property of equality
Step-by-step explanation:
x/4=36/16
Cross product
16*x=36*4
16x=144
Divide both sides by 16
x=144/16
=9
What property allowed her to go from
x/4=36/16
To
x/4*4=36/16*4
Multiplication property of equality would allow her to go from
x/4=36/16
To
x/4*4=36/16*4
Answer:
multiplication property of equality
Step-by-step explanation:
what is the value of x if the LCM of x and 84 is 1260 ,x is odd number
Answers
Answer:
X=15
Step-by-step explanation:
1260/84=15
because 25 percent of the students in my morning statistics class watch eight or more hours of television a week, i conclude that 25 percent of all students at the university watch eight or more hours of television a week. the most important logical weakness of this conclusion would be
Answers
The main logical weakness of the conclusion is the hasty generalization made from a potentially unrepresentative sample. To strengthen the argument, a more comprehensive survey of the university's student population should be conducted.
The most important logical weakness of the conclusion that "25 percent of all students at the university watch eight or more hours of television a week" based on the observation from your morning statistics class is that it involves a hasty generalization.
A hasty generalization occurs when you draw a conclusion about a larger group based on a smaller, unrepresentative sample. In this case, the student question assumes that the morning statistics class is representative of the entire university, which may not be true.
To better explain this logical weakness, let's break down the steps:
The student observes that 25 percent of the students in their morning statistics class watch eight or more hours of television a week.
The student then concludes that this must apply to all students at the university.
The conclusion does not account for potential differences between the morning statistics class and other classes or students at the university.
To overcome this logical weakness, a more representative sample of the university's student population should be surveyed to accurately determine the percentage of students who watch eight or more hours of television a week. This might involve selecting students from different majors, class schedules, and demographic backgrounds to ensure that the sample truly represents the entire university population.
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Solve the inequality 7≥b+-2
Answers
Answer:
9 is greater than or equal to b
Step-by-step explanation:
7 is greater than or equal to b+-2
(Add two to both sides)
9 is greater than or equal to b
Hope this helps
The box plots show the average speeds, in miles per hour, for the race cars in two different races. Average Speeds of Cars in Race A 2 box plots. The number line goes from 120 to 170. For Race A, the whiskers range from 120 to 170, and the box ranges from 143 to 165. A line divides the box at 153. For Race B, the whiskers range from 125 to 165, and the box ranges from 140 to 150. A line divides the box at 145. Average Speeds of Cars in Race B
Answers
Answer:
The median speed in race A is about 153 miles per hour, and the median speed in race B is about 145 miles per hour.
Step-by-step explanation:
For comparison, we need to analyze and compare both races data which are as follows
For Race A
Maximum range = 170 miles per hour
Minimum range = 120 miles per hour
First quartile ≈ 142 miles per hour
Median quartile ≈ 153 miles per hour
It comes from
\(= \frac{142\ miles + 165\ miles}{2}\)
= 153 miles
The Third quartile = 165 miles per hour
For Race B
Maximum range = 165 miles per hour
Minimum range = 125 miles per hour
First quartile ≈ 139 miles per hour
Median quartile = 145 miles per hour
It comes from
\(= \frac{139\ miles + 150\ miles}{2}\)
= 145 miles
The third quartile = 150 miles per hour
Hence, the last option is correct