Since the bias of u1 depends on the true value of the parameter θ, we cannot determine whether any particular point estimate is unbiased without knowing θ. However, we can say that u1 is not generally an unbiased estimator, since its bias is a non-zero function of θ.
Assuming we do know the true value of the parameter, the bias of a point estimate is given by the difference between the expected value of the estimator and the true value of the parameter. Specifically, the bias of an estimator E(θ) is given by:
Bias(E(θ)) = E(E(θ)) - θ
where θ is the true value of the parameter.
In the case of the estimator u1, we have:
E(u1) = E(x1/4 + x2/3 + x3 + 5) = 1/4 E(x1) + 1/3 E(x2) + E(x3) + 5
If we assume that x1, x2, and x3 are independent and identically distributed (i.i.d.), then we can use the linearity of expectation to simplify this expression
E(u1) = 1/4 E(x1) + 1/3 E(x2) + E(x3) + 5
= 1/4 θ + 1/3 θ + θ + 5
= 17/12 θ + 5
where θ is the true value of u1.
Therefore, the bias of u1 is:
Bias(u1) = E(u1) - θ
= (17/12 θ + 5) - θ
= 5/12 θ + 5
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Question
Suppose you have a set of data points {x1, x2, x3}. Calculate the bias of each point estimate of the following parameter:
u1 = x1/4 + x2/3 + x3 + 5
To calculate the bias of each point estimate, we first need to know the true population parameter that we are trying to estimate. Without that information, we cannot determine if any of the point estimates are unbiased.
Assuming we are trying to estimate the population mean, μ, based on the sample means x1, x2, and x3, we can rewrite the formula for u1 as:
u1 = (1/4)x1 + (1/3)x2 + x3 + 5
The bias of a point estimate is the difference between the expected value of the estimate and the true value of the parameter being estimated. In other words, if we were to take many samples from the population and calculate the mean of each sample, the bias of a particular point estimate would be the difference between the average of all those sample means and the true population mean.
Without knowing the true population mean, we cannot calculate the bias of each point estimate. However, we can say that if the expected value of any of the point estimates is equal to the true population mean, then that point estimate is unbiased.
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Brass is made up of copper and zinc. 100 grams of brass contains 20 grams of zinc.
A) Workout the weight of zinc in 60 grams of brass.
Brass contains 4 parts by weight of copper to 1 part by weight of zinc.
B) Work out the weight of copper in 350 grams of brass.
Answer:
A. 12 grams Zn
B. 280 g of copper.
Step-by-step explanation:
100 grams of brass
20 grams of zinc
100 grams of brass has 20 grams of Zn.
20/100 = 0.200 Zn 20% Zn and 80% copper.
A. (60 g brass)*(0.2) = 12 grams Zn
B. (350 g brass)*(0.80) = 280 g of copper.
A has the coordinates (-4, 3) and B has the
coordinates (4, 4). If Do,1/2(x, y) is a dilation of AABC,
what is true about the image AA'B'C'? Check all that
apply.
If [tex]$D_{o,\frac{1}{2}} \frac{1}{2} (x, y)[/tex] exists a dilation of △ ABC, the facts regarding the image
△A'B'C' exist AB exists parallel to A'B'.
What is a coordinate plane?Any point in the coordinate plane exists directed by a point (x, y), where the x value exists the position of the point with respect to the x-axis, and the y value exists the position of the point with respect to the y-axis.
A dilation exists a transformation [tex]$D_{o,k} \frac{1}{2} (x, y)[/tex], with center O and a scale factor of k that exists not zero, that maps O to itself and any other point P to P'. The center O exists as a fixed point, P' exists as the image of P, and points O, P, and P' exist on the exact line.
In a dilation of [tex]$D_{o,\frac{1}{2}} \frac{1}{2} (x, y)[/tex], the scale factor, 1/2 exists mapping the original figure to the image in such a manner that the distances from O to the vertices of the image exist half the distances from O to the original figure.
Also, the size of the image exists half the size of the original figure.
If [tex]$D_{o,\frac{1}{2}} \frac{1}{2} (x, y)[/tex] exists a dilation of △ ABC, the facts regarding the image △A'B'C' exist AB is parallel to A'B'.
[tex]$D_{o,k} \frac{1}{2} (x, y) = (\frac{1}{2} x, \frac{1}{2}y)[/tex]
The distance from A' to the origin exists half the distance from A to the origin.
Therefore, the correct answer is option A). △ A'B'C' exist AB is parallel to A'B'.
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Suppose the variable x is represented by a standard normal distribution. What value of x is at the 40th percentile of the distribution
The value value of x is at the 40th percentile of the distribution is 0.65.
The standard normal distribution is a normal distribution with a mean of zero and standard deviation of 1. The standard normal distribution is centered at zero and the degree to which a given measurement deviates from the mean is given by the standard deviation
Given:- μ[tex]_X[/tex]=0,σ[tex]_X[/tex]=1
We can standardize the random variable: Z=(X−μx)/σx,
Then the equation is P(X≤ x )=Φ(x−μx/σx)=Φ(x−0/1)=0.4
Inverse function
Ф[tex]\\^{-1}[/tex](0.4) = [tex]\frac{x-0}{1}[/tex]
From the table we get,
Ф[tex]^{-1}[/tex] = 0.65
Thus
[tex]\frac{x-40}{10}[/tex] = 0.65
x -0 = 0.65
x = 6.5
Thus the value value of x is at the 40th percentile of the distribution is 0.65
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6,000 people voted in a town election. Of the two candidates, the winning candidate received 4,000 more votes than the losing candidate. How many votes did the winner get?
Answer:
Step-by-step explanation:
let x = the number of votes of the first person
winner = x + 4000
x+ x+4000 = 6000
2x=2000
x=1000
first person = x = 1000
winner = x+4000 = 5000
The winner got 5000 votes
In apirl is rained 1/4 of a inch on 15 diffret day how many inches of rain fell
In [tex]15[/tex] diffret days [tex]15/4[/tex] inches of rain fell in April month if every day rained [tex]1/4[/tex] of a inch .
How to find the rain fell in [tex]15[/tex] diffret days ?
We know that rain in every day is [tex]1/4[/tex] of a inch
So for [tex]15[/tex] days
[tex]1/4+1/4+1/4+......15times\\=15/4[/tex]
So in [tex]15[/tex] diffret days in April rain fell is [tex]15/4[/tex] inches.
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Lowest common multiple of 12,18,56
Step-by-step explanation:
12 = 2 × 2 × 3
18 = 2 × 3 × 3
56 = 2 ×2 × 2 × 7
Now
Common factor = 2
Remaining factor = 2 × 3 × 2 × 3 × 7
LCM = RF × CF
= 504
hence the lCM of 12 , 18 and 56 is 504...
[tex]...[/tex]
Which describes Which is a perfect square?
72
81
90
99
Answer:
81
Step-by-step explanation:
A perfect square is multiplying a number with the same number in question. 81 is a perfect square because either 9 or -9 will go into it perfectly, like a square's length and height.
[tex]9^{2} = 81[/tex]
Answer: 81
Step-by-step explanation:
81 can be perfectly square rooted into 9. [tex]\sqrt{81}=9[/tex]
Segment ab falls on line 6x 3y = 9. segment cd falls on line 4x 2y = 8. what is true about segments ab and cd? they are parallel because they have the same slope of −2. they are perpendicular because they have slopes that are opposite reciprocals of −2 and one half. they are parallel because they have the same slope of 2. they are perpendicular because they have opposite reciprocal slopes 2 and negative one half.
They are parallel because they have the same slope of 2.
How to determine the true statements about the segments?The segments are given as;
AB => 6x - 3y = 9
CD => 4x - 2y = 8
We start by making y the subject of both equations
AB => 6x - 3y = 9
-3y = -6x + 9
Divide through by -3
y = 2x - 3
CD => 4x - 2y = 8
-2y = -4x + 8
Divide through by -2
y = 2x - 2
A linear equation is represented as:
y = mx + b
Where m represents the slope of the line.
By comparing the three equations, we have:
m1 = 2
m2 = 2
Parallel lines have equal slopes.
This means that the lines AB and CD are parallel lines
Hence, they are parallel because they have the same slope of 2.
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Answer: They are parallel because they have the same slope of 2.
Step-by-step explanation:vvvvvvvvvvvvvvvvvvvvv
True or false, if a domain is restricted to x > 1, then there will be an open circle at x = 1.
Answer:
Step-by-step explanation:
true
If sin (90° - α) = BC /CA,write down the ratio of sina.
Answer:
Step-by-step explanation:
sin(90-a)=cos
cos = angle adjacent
theta=BC/CA
HELP FAST‼️‼️
Jessenia usually earns $25 each week.
Last week, she received an extra $20 in
bonus. What percent of her usual weekly
income was her total income last week?
Normal income: 25 $
Last week's income: 25 + 20: 45 $
% = Last week's/normal = 45/25 ×100 =180 %
Mary performs this calculation. (3.0) (2.0). how many significant figures should her answer have? one two four six
Answer:
2
Step-by-step explanation:
There are only 2 numbers in the final answer (6.0), so you just need 2 significant figures.
Need help with explanation on solving this problem.
Answer:
x=27.80
Step-by-step explanation:
we know that cosA=base/hypotaneous
so,
[tex]cos44 = \frac{20}{x} \\ x = \frac{20}{cos(44)} \\ = \frac{20}{0.7193...} \\ = 27.80 [/tex]
A safe has a 4-digit lock code that does not include zero as a digit and no digit is repeated. what is the probability that the lock code consists of all even digits?
Probability that the lock code consists of all even digits is [tex]1344[/tex] if we choose the [tex]4[/tex] digit lock is randomly from numbers [tex]1,2,3,4,5,6,7,8,9[/tex]
How can we find the probability that the lock code consists of all even digits?
Total numbers are [tex]1,2,3,4,5,6,7,8,9[/tex]
And we choose [tex]4[/tex] digit code
So probability of choosing [tex]4[/tex] numbers from [tex]9[/tex] numbers without reapitation is
[tex]9p_{4} =\frac{9!}{(9-4)!} \\=\frac{9*8*7*6*5!}{5!} \\=3024[/tex]
For All numbers are even , probability the last digit of number is even.
So we have [tex]4[/tex] even number and if we fix one on last digit and can change other [tex]3[/tex] then the probability is
[tex]4*8P_{3} =4*\frac{8!}{(8-3)!} \\=4*\frac{8*7*6*5!}{5!} \\=1344[/tex]
So the total probability of code lock having all even number is [tex]1344[/tex]
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You and a friend are playing a game of chance. Every time you roll a 1 or 2 you are successful, and your friend will pay you $1. Every time you roll (using a fair die) a 3, 4, 5 or 6, you must pay your friend $2. If 71% of your rolls are successful and 29% of your rolls are unsuccessful, how much money do you expect to have earned/owed by the end of the game
Considering the mean of a discrete distribution, you are expected to earn $0.13 by the end of the game.
What is the mean of a discrete distribution?The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.
Since 71% of your rolls are successful and 29% of your rolls are unsuccessful, the distribution of your earnings is:
P(X = 1) = 0.71.P(X = -2) = 0.29Hence the expected value is:
E(X) = 1 x 0.71 - 2 x 0.29 = 0.71 - 0.58 = 0.13
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someone please help asap.. what even is this. ill give brainliest
Given: line AC is perpendicular to line BC
Prove: the slopes of lines AC and BC is -1
Complete the Proof.
first blank: angle addition; definition of perpendicular lines; definition of congruent angles; definition of a straight angle.
second blank: addition property of equality; subtraction property of equality; transitive property of equality; substitution property of equality.
third blank: transitive property of equality; substitution property of equality; definition of slope; corresponding sides of similar triangles are proportional.
fourth blank: multiplication property of equality; substitution property of equality; addition property of equality; transitive property of equality.
Congruency property relates to two or more triangles with similar dimensions, and internal angles. So that the required statements to complete the proof are:
1. definition of a straight angle.
2. subtraction property of equality
3. corresponding sides of similar triangles are proportional
4. transitive property of equality.
The intersection of two or more lines forms a number of angles which depends on the number of lines involved. These angles formed may have similar or different properties.
When two or more triangles have similar lengths of sides and measure internal angles, it can be said that they are congruent. Thus they have some common properties.
Therefore, the appropriate statements to answer the given question are stated below:
Definition of a straight angle.Subtraction property of equality.Corresponding sides of similar triangles are proportional.Transitive property of equality.For more clarifications on the properties of congruent triangles, visit: https://brainly.com/question/15835221
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What is the area of a square with a perimeter of 44 mm?
Answer:
The area of the square is 121mm
Step-by-step explanation:
To solve this we need two basic formulas:
P = 4s
A = [tex]s^{2}[/tex]
P = perimeter
s = the length of the side
Since the shape is a square all the sides are the same length. To get the value of 's' we need to isolate:
P = 4s
44 = 4s
44 / 4 = 4s / 4
11 = s
Now plug in the answer for 's' to get the area:
A = [tex]s^{2}[/tex]
A = [tex]11^{2}[/tex]
A = 121
Hope this helps.
A construction company buys a certain number of boxes of nails depending on how many houses they plan to build in a year. They have 5 boxes left over from the previous year and predict that this year they will need 3 boxes per house. Write an equation where y represents the number of boxes they need to purchase and x the number of houses they plan to build.
Answer:
Step-by-step explanation:
43
I dont exactly know if this is correct sorry if its wrong
Can you plssss help !!!
The parts of the circle shown in the image include, chord, diameter, radius, tangent and center point.
Parts of the circle shown in the imageThe following are the parts of the circle shown;
Chord: the length DC and DG represent the chord of the circleDiameter: the length HF represent the diameter of the circleRadius: the length HA and FA represents the radius of the circletangent: the line JB represents a tangent to the circleCenter: point A represents the center of the circleThus, the parts of the circle shown in the image include, chord, diameter, radius, tangent and center point.
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Help pls
Use the data from the table to create a scatter plot. Plot all the data points from the table.
Variable A 1 4 2 3 5 1 3 7 6 6 2 9 7 5 8
Variable B 6 6 1 6 7 4 4 7 5 3 5 25 21 4 4
The attached graph represents the scatter plot of the table of values
How to create the scatter plot?The table of values is given as:
Variable A 1 4 2 3 5 1 3 7 6 6 2 9 7 5 8
Variable B 6 6 1 6 7 4 4 7 5 3 5 25 21 4 4
Rewrite the table as:
x 1 4 2 3 5 1 3 7 6 6 2 9 7 5 8
y 6 6 1 6 7 4 4 7 5 3 5 25 21 4 4
Next, we plot the values on a graph
See attachment for the scatter plot
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The 3 stages representing the hierarchy of fluency progression including Automaticity, are embedded into which strand of the B.E.S.T. mathematics standards
The three stages that have to do with fluency, progression and automaticity are found in the Number Sense and Operations .
What is the number sense and operation strand of mathematics?This is the part of mathematics that is known to teach the student basic ways to carry out number operations in mathematics. This has to do with representation of numbers as well as solving for the existing relationships in these numbers.
Having a sense of numbers is a very important ability skill that has to be developed early is students to enable them progress in the subject.
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Unoccupied seats on flights cause airlines to lose revenue. Suppose a large airline wants to estimate its mean number of unoccupied seats per flight over the past year. To accomplish this, the records of 225 flights are randomly selected and the number of unoccupied seats is noted for each of the sampled flights. The sample mean is 11.6 seats and the sample standard deviation is 4.1 seats. Assume the underlying population of unoccupied seats is normally distributed. Using a t- statistic, construct a 95% confidence interval for the population mean number of unoccupied seats per flight.
The given sample's 95% confidence interval is 11.6 ± 0.5357. I.e., from the lower bound 11.06 to the upper bound 12.14. Its margin error is 0.5357.
How to find the confidence interval?To find the confidence interval C.I,
Determine the mean(μ) of the sampleDetermine the standard deviation(σ)Determine the z-score for the given confidence level using the z-score tableUsing all these, the confidence interval is calculated by the formula, C. I = μ ± z(σ/√n) where n is the sample size and z(σ/√n) gives the margin error. So, we can also write C. I = mean ± margin error.Calculation:It is given that,
Sample size n = 225
Sample mean μ = 11.6
Standard deviation σ = 4.1
Since 95% confidence interval, z-score is 1.96
So, the required confidence interval is calculated by,
C. I = μ ± z(σ/√n) or mean ± margin error
On substituting,
C. I = 11.6 ± 1.96(4.1/√225)
= 11.6 ± 1.96 × 0.2733
= 11.6 ± 0.5357
So, the lower bound = 11.6 - 0.5357 = 11.065 and
the upper bound = 11.6 + 0.5357 = 12.135.
Thus, the confidence interval is from 11.06 to 12.14, and its margin error is 0.0537 for the population mean number of unoccupied seats per flight.
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Elena is making an open-top box by cutting squares out of the corners of a piece of paper that is 11 inches wide and 17 inches long, and then folding up the sides. If the side lengths of her square cutouts are inches, then the volume of the box is given by V(x)=(11-2x)(17-2x).
There are 4 questions in the bottom! Please solve and explain them for me!
Thank youuu
See below for the solution to each question
The reasonable domain of V(x)From the graph, we can see that:
V(x) have a positive value from x > 0 to x < 5.5
When x = 0 and ≥ 5.5, the values of V(x) are either 0 or negative
Hence, the reasonable domain of V(x) is 0 < x < 5.5
The value of x that gives the maximum volumeFrom the graph, the maximum value of V(x) is at
V(2) = 182
Hence, the approximate value of x that gives the maximum volume is 2
The values of x where the volume increasesThis is the interval where V(x) increase as x increase
From the graph, V(x) increase from x > 0 to x = 2
Hence, the approximate values of x where the volume increases are 0 < x ≤ 2
The interpretation of the point of intersectionThe other function is
B(x) = 140
So, the point of intersection represent where the volume is 140
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PLEASE HELP IM REALLY STUCK
Answer:
[tex]a_{18}=-70[/tex]
Step-by-step explanation:
[tex]a_n=a_1+(n-1)d[/tex]
[tex]a_1=2, d = -4[/tex]
[tex]a_{18}=-2+(18-1)*(-4)=-2-68=-70[/tex]
What is the measure of arc QR?
Answer:
answer is the third choice : 104
Step-by-step explanation:
Inscribed Angle Theorem
If an angle is inscribed in a circle, then the measure of the angle equals one half the measure of its intercepted arc.
so the intercepted arc is TWICE the measure of an angle inscribed in a circle
1. A central angle is an angle with endpoints located on a circle's circumference and vertex located at the circle's center. A central angle in a circle determines an arc.
2. An inscribed angle is an angle formed by three points on the circle's circumference.
Angle at the Center Theorem: An inscribed angle is half of the central angle (if they determine the same arc).
In your case angles:
1. ∠QSR is insribed (determines the arc QR);
2. ∠QTR is central (determines the arc QR).
Then by Angle at the Center Theorem, m∠QTR=2m∠QSR=2·52°=104°. Arc QR has the same measure as central angle QSR.
gathmath
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4x-6y=-20
-2x+4y=6
8th grade pre algebra
The values of x and y that are solutions to the simultaneous equations are; x = -11 and y = -4
How to Solve Simultaneous Equations?
We are given the simultaneous equations;
4x - 6y = -20 -----(eq 1)
-2x + 4y = 6 -----(eq 2)
Multiply equation 2 by 2 and eq 1 by 1 to get;
-4x + 8y = 12 -----(eq 3)
Add eq 3 to eq 1 to get;
2y = -8
y = -4
Thus;
4x - 6(-4) = -20
4x + 24 = - 20
4x = -20 - 24
4x = -44
x = -44/4
x = -11
Thus, the values of x and y that are solutions to the simultaneous equations are; x = -11 and y = -4
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It cost Cai $1,80 to send 12 text messages, How much would it cost to send 90 text
messages?
Answer:
$13.5
Step-by-step explanation:
cost of 1 text message= $1.80÷12 =$0.15
cost of 90 messages = $0.15×90 = $13.5
Answer: $13.50 for 90 text messages
Step-by-step explanation:
$0.15×90 = $13.5
$0.15 is the unit rate for 1 text message cost.
Which algebraic expression has a term with a coefficient of 9?
• A. 6 + X- 9
• B. 6x - 9
C. 6(x + 5)
• D. 9x ÷ 6
[tex]\textbf{ Heya !}[/tex]
Your Answer Is:-
[tex]\sf{9x\div6}[/tex]
because,
it has a coefficient of 9 (a number that comes before a variable)
`hope that was helpful to u ~
Here is a rail way timetable
What time does the first train get to oakengats?
The time that the first train would get to Oakengats is 08:15.
How to find the time of arrivalThe time of arrival of the first train can be gotten from the table.
The first entry has a blank space. This would have been the time of arrival for the train.
After the blank space, the next time is when the fits train got to this destination. That is at 08:15
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someone please help me with question #14 !!!
Answer: a, c, e
Step-by-step explanation:
a) True. If x=0, f(0)=c.
b) False. Considering the quadratic formula, we know the solutions are not always x=c.
c) True. This is a standard fact.
d) False. If the discriminant is not positive, there are less than two x-intercepts.
e) True. If you plug into the formula [tex]x=-\frac{b}{2a}[/tex], if b=0, then obviously the x-coordinate of the vertex is also 0.