Answer:
The method of moment (MOM) estimator as: [tex]\mathbf{\hat {\theta} =(\dfrac{\overline X}{1-\overline X})^2}[/tex]
[tex]\overline X = \dfrac{4}{9}[/tex]
[tex]\mathbf{\hat {\theta} =\dfrac{16}{25} }[/tex]
Step-by-step explanation:
From the question, the correct format for the probability density function is:
[tex]fx(x ; \theta) = \left \{ {{\sqrt{\theta x}^{\sqrt{\theta}-1}}\ \ 0 \leq x \leq 1 \atop {0} \ \ \ \ \ \ \ otherwise } \right.[/tex]
where θ > 0 is an unknown parameter.
(a) The MOM estimator can be calculated as follows:
[tex]E(X) = \int ^1_0x. \sqrt{\theta} \ x^{\sqrt{\theta}-1} \ dx[/tex]
[tex]E(X) = \int ^1_0 \sqrt{\theta} \ x^{\sqrt{\theta}} \ dx[/tex]
[tex]E(X) = \dfrac{\sqrt{\theta} }{\sqrt{\theta} +1 } ( x ^{\sqrt{\theta}+1})^1_0[/tex]
[tex]E(X) = \dfrac{\sqrt{\theta} }{\sqrt{\theta} +1 }[/tex]
suppose E(X) = [tex]\overline X[/tex]
Then;
[tex]\overline X = \dfrac{\sqrt{\theta} }{\sqrt{\theta} +1 }[/tex]
[tex]\dfrac{1}{\overline X} = \dfrac{\sqrt{\theta} +1 }{\sqrt{\theta}}[/tex]
[tex]\dfrac{1}{\overline X} =1 + \dfrac{1}{\sqrt{\theta}}[/tex]
making [tex]\dfrac{1}{\sqrt{\theta}}[/tex] the subject of the formula, we have:
[tex]\dfrac{1}{\sqrt{\theta}} =\dfrac{1}{\overline X} - 1[/tex]
[tex]\dfrac{1}{\sqrt{\theta}} =\dfrac{1-\overline X}{\overline X}[/tex]
[tex]\sqrt{\theta} =\dfrac{\overline X}{1-\overline X}[/tex]
squaring both sides, we have:
The method of moment (MOM) estimator as: [tex]\mathbf{\hat {\theta} =(\dfrac{\overline X}{1-\overline X})^2}[/tex]
b) If the observations are [tex]\dfrac{1}{2}, \dfrac{1}{3}, \dfrac{1}{2}[/tex]
Then,
[tex]\overline X = \dfrac{\dfrac{1}{2}+ \dfrac{1}{3}+\dfrac{1}{2}}{3}[/tex]
[tex]\overline X = \dfrac{\dfrac{3+2+3}{6}}{3}[/tex]
[tex]\overline X = \dfrac{\dfrac{8}{6}}{3}[/tex]
[tex]\overline X = \dfrac{8}{6} \times \dfrac{1}{3}[/tex]
[tex]\overline X = \dfrac{8}{18}[/tex]
[tex]\overline X = \dfrac{4}{9}[/tex]
Finally, the point estimate of the estimator [tex]\theta[/tex] is
[tex]\mathbf{\hat {\theta} =\begin {pmatrix} \dfrac{\dfrac{4}{9}}{1-\dfrac{4}{9}} \end {pmatrix}^2}[/tex]
[tex]\mathbf{\hat {\theta} =\begin {pmatrix} \dfrac{\dfrac{4}{9}}{\dfrac{5}{9}} \end {pmatrix}^2}[/tex]
[tex]\mathbf{\hat {\theta} =\begin {pmatrix} \dfrac{4}{5} \end {pmatrix}^2}[/tex]
[tex]\mathbf{\hat {\theta} =\dfrac{16}{25} }[/tex]
plz click this help me and i am really desspprte and i do not want get in trouble plz my teacher is very strict.
someone said this was wrong and I realized that I was just confused so i fixed it
it's 3:1
Answer:
b
Step-by-step explanation:
Camden drove 320 miles in 8 hours. If he continued at the same rate, how far would he travel in 7 hours?
Answer:
280 miles
Step-by-step explanation:
We want to determine what speed Camden is going first so we can find the distance. To do so, you can divide the total miles (320) by the number of hours (8) to find he is driving 40 miles per hour. Then, you can take that and multiple it by the number of hours he will drive (7) to get 280 miles. I hope this helps! :)
What is the image of T( -4,0) under the rule (x - 7, y)
Answer:
Step-by-step explanation:
I know the answer but can not create it on here sorry....Brighton Company launched a new gaming console. They sold 200 consoles prior to the launch.
The number of consoles sold each day after the launch is shown by the graph below.
Answer: in the domain of this situation, there is no asymptote.
Step-by-step explanation:
Asymptote would be on the left where x is negative but this function only shows all positive values of X
The value of k is -0.25. The graph shows that the actual number of consoles sold is slightly higher than the predicted number of consoles sold.
The graph shows that the number of consoles sold each day after the launch of the Brighton Company gaming console follows an exponential decay pattern. This means that the number of consoles sold each day is decreasing at a rate that is proportional to the number of consoles that have already been sold.
The equation that can be used to model this exponential decay pattern is:
N = A * [tex]e^{-kt[/tex]
where:
N is the number of consoles sold on day t
A is the initial number of consoles sold (200 consoles)
k is a constant that determines the rate of decay
e is the base of the natural logarithm
We can use the data from the graph to estimate the value of k. The first day after the launch, 180 consoles were sold. This means that on day 1, N = 180. The initial number of consoles sold, A, is known to be 200 consoles. Therefore, we can write the following equation:
180 = 200 * [tex]e^{-kt[/tex]
Solving for k, we get:
k = -ln(1.8) / 1
≈ -0.25
The value of k is approximately -0.25. This means that the number of consoles sold each day is decreasing at a rate of 25%.
We can use the equation to predict the number of consoles sold on future days. For example, on day 2, we would predict that 150 consoles would be sold. On day 3, we would predict that 120 consoles would be sold.
The graph shows that the actual number of consoles sold is slightly higher than the predicted number of consoles sold. This is because the exponential decay pattern is not perfect. There are other factors that can affect the number of consoles sold, such as the availability of the console and the price of the console.
To learn more about graph here:
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An organism measures 2.9• 10-5 centimeters in diameter. What number in standard notation [ANSWERS PLEASE I’ll even cash app u 2$]
The temperature in Chicago was 12°F this
morning, while the temperature in Minneapolis
was -8°F. What is the difference between the
two temperatures?
Answer:
4 °F
Step-by-step explanation:
In a hotel a servant needs to clean 30 rooms in 3 hours. How many rooms a servant needs to clean in 6 hours
Answer: 60 rooms
Step-by-step explanation:
because in 30 rooms is 3 hour + other 3 hour are 60 rooms. =60 rooms
Suppose you've just deposited $ 2,004 in a bank account which earns an annual rate of return of 12%. How much will you have in the bank account after 5 years
Answer:
you will get back 167$
Step-by-step explanation:
The 2nd one is right just did the test
Answer:
ok lol
Step-by-step explanation:
Answer:
Is it just me or after this did you just put the 2nd answer for every question after this and failing every test I have taken
Step-by-step explanation:
How many cups of flour are needed to make 3 dozens of dinner rolls
Answer: 1/15
Step-by-step explanation: A. If 1/3 cup makes 5 rolls, you need to know how many cups make one. (1/3)/5 = 1/15 Take the number of cups for one roll and multiply it by 3. 1/15 x 3 Final Answer = 3/15
B. Take the number of cups you have divided by 1/3 (since you know how many roles this makes) (5 2/3) / (1/3) Final Answer = 17
C. Well, we already solved for this one in A, didn't we? Final Answer = 1/15
Which THREE storage devices are non-volatile? Non-volatile devices can store data regardless of whether they are powered on or not.
thumb drive
RAM
hard disk
ROM
Answer: Thumb drive, ROM, Hard-disk
Step-by-step explanation:
Chris has 5 1/2cups of water in a pitcher. He pours 3/8 cup of water into a glass. How many cups of water is left in the pitcher? Enter your answer in the box as a mixed number in simplist form?
Answer: The Answer is 5 1/8.
Step-by-step explanation:
Please help. Don’t understand this math problem
Answer:
-24r + 56
Step-by-step explanation:
To find the area of this rectangle we multiply width and length
8 × (-3r + 7) = -24r + 56
Between what two integers does the square root of 14 lie?
Answer:
3 and 4
Step-by-step explanation:
30 divided by 1.25 with work
Answer:
24
Step-by-step explanation:
If you need an explaination you should immediatly remove yourself from the Gene pool, this is a 3rd grade question.
The result is: 30 divided by 1.25 equals 24.
To divide 30 by 1.25, follow these steps in words:
The division 30 ÷ 1.25 can be written as the fraction 30/1.25.
Remove the decimal by multiplying both the numerator and denominator by a power of 10 to convert the decimal into a whole number.
Since 1.25 has two decimal places, multiply both the numerator and denominator by 100 to remove the decimal:
30/1.25 = (30 * 100) / (1.25 * 100) = 3000 / 125
Find the greatest common divisor (GCD) of the numerator and denominator and divide both by the GCD to simplify the fraction:
GCD of 3000 and 125 is 25.
3000 ÷ 25 = 120
125 ÷ 25 = 5
So, 3000/125 simplifies to 120/5.
Divide the numerator by the denominator to get the final result.
Now, simply divide the numerator (120) by the denominator (5):
120 ÷ 5 = 24
The result is 24.
So, 30 divided by 1.25 equals 24.
To learn more on division click:
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sin3A/sinA-Cos3A/CosA=2
Answer:
sin3A/sinA-Cos3A/CosA=2
taking LCM
= Sin3A.CosA - Cos3A. SinA
SinA . CosA
= Sin(3A-A)
SinA . CosA
= Sin2A
SinA . CosA
= 2 SinA. CosA
SinA . CosA
=2
Step-by-step explanation:
What is the value of x in the equation 3x – one-ninthy = 18, when y = 27? 5 7 45 63
Answer:
7
Step-by-step explanation:
3x – one-ninthy = 18, when y = 27?
one-ninthy 27 = 3
3x - 3 = 18
3 x 7 = 21
21 - 3 = 18
hope this helps
Answer:
7
Step-by-step explanation:
answered on edge
100 POINTS!!! ASAP-- Pls show work too TY
Answer:
I will help you but is there any picture that can help me answer the question?
Answer:
[tex]\sin(\theta)=\frac{\sqrt{13}}{7}\approx0.5151[/tex]
Step-by-step explanation:
So we know that Θ is acute and that:
[tex]\cos(\theta)=6/7[/tex]
First, note that since Θ is acute, it is between 0 and 90 degrees, meaning that all of our trig ratios will be positive since the angle is in the Quadrant I.
The Pythagorean Identity is:
[tex]\sin^2(\theta)+\cos^2(\theta)=1[/tex]
We know that cosine is 6/7. Substitute:
[tex]\sin^2(\theta)+(\frac{6}{7})^2=1[/tex]
Square:
[tex]\sin^2(\theta)+\frac{36}{49}=1[/tex]
Subtract both sides by 36/49. Change the 1 to 49/49 to make a common denominator:
[tex]\sin^2(\theta)=\frac{49}{49}-\frac{36}{49}[/tex]
Subtract:
[tex]\sin^2(\theta)=\frac{13}{49}[/tex]
Take the square root of both sides:
[tex]\sin(\theta)=\pm\sqrt{\frac{13}{49}}[/tex]
Simplify:
[tex]\sin(\theta)=\pm\frac{\sqrt{13}}{7}[/tex]
As mentioned previously, since Θ is acute, all of the trig functions must be positive. So, we can ignore our negative answer:
[tex]\sin(\theta)=\frac{\sqrt{13}}{7}\approx0.5151[/tex]
and we're done!
On Thursday, a local hamburger shop sold a combined total of 580 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Thursday?
Answer:
Hey there!
Let h be the number of hamburgers sold.
Let c be the number of cheeseburgers sold.
h+c=580
c=3h
4h=580
h=145
145 hamburgers were sold.
Let me know if this helps :)
. Pay close attention to the order operations to find the value of: 26 + (10-2) = 4 + 3 - 6 Show each step:
Angle RST below is a right angle. What is the measure, in degrees, of
Answer:
RSM = 56.4
Step-by-step explanation:
RSM + MST = RST
RSM + 33.6= 90
Subtract 33.6 from each side
RSM + 33.6 - 33.6= 90-33.6
RSM= 90-33.6
RSM = 56.4
RST is a right angle, and right angles are 90 degrees
RST = 90 degrees
MST = 33.6 degrees
RSM = ?
The angles MST and RSM add up to 90 degrees
90 = 33.6 + RSM
Subtract 33.6 from both sides
56.4 degrees = RSM
Choose the expression that represents the prime factorization of 96.
3.24
6.8.2
3.25
3.2.2.2.2
Answer:
3.2.2.2.2...
Step-by-step explanation:
The prime factors of 96 are written as 2 x 2 x 2 x 2 x 2 x 3 or 3 x 25, where 2 and 3 are the prime numbers
Alicia answered 20 out of 25 problems correctly on a test. What percent did she get correct?
Answer:
80
Step-by-step explanation:
20 / 25 = 0.8 = 80%
Answer:
80%
Step-by-step explanation:
20/25 = 0.8 = 80%
Find the value of the variables in the figure to the right.
Answer:
x = 9
y = 56
Step-by-step explanation:
(3x + 7)° + (6x + 2)° = 90° (both angles are complementary)
Find the value of x using this equation
[tex] 3x + 7 + 6x + 2 = 90 [/tex]
Collect like terms
[tex] 3x + 6x + 7 + 2 = 90 [/tex]
[tex] 9x + 9 = 90 [/tex]
Subtract 9 from each side
[tex] 9x + 9 - 9 = 90 - 9 [/tex]
[tex] 9x = 81 [/tex]
Divide both sides by 9
[tex] \frac{9x}{9} = \frac{81}{9} [/tex]
[tex] x = 9 [/tex]
y° = (6x + 2)° (both angles are vertical angles. Vertical angles are equal)
Plug in the value of x to find y
y = 6(9) + 2
y = 54 + 2
y = 56
Ms. Albero decided to make juice to serve along with the pizza at the Student Government party. The directions said to mix 2 scoops of powdered drink mix with a half gallon of juice. One of Ms. Albero's students said show will mix 8 scoops with 2 gallons of water to make 4 pitchers. How can you use the concept of proportional relationships to decide whether the student is correct? *
Answer:
Yes, the student is correct.
Step-by-step explanation:
2*4=8 scoops
1/2*4=2 gallons
Since they were multiplied by the same number, the student is correct. It's like making it 4 times, but all at once.
I hope this was helpful!
There are 75 students in a speech contest. Yesterday, 2/5 of them gave their speeches. Today, 1/3
of the remaining students gave their speeches. How many students still haven't given their speeches?
Work Shown:
2/5 of 75 = (2/5)*75 = 0.4*75 = 30
Yesterday 30 people gave speeches. There are 75-30 = 45 people left.
1/3 of 45 = (1/3)*45 = 15
Then another 15 people gave speeches today. So there are 45-15 = 30 people who haven't given their speeches yet.
What is the inverse of f(x) = 2x+ 2?
Help ASAP please please
Answer:
5/6
Step-by-step explanation
4= 6/a x +5
solve for x
The ratio of 1.4 to 29 is the same as the ratio of 2.8 to
Answer: Is the same as 2.8 to 58
Step-by-step explanation:
The ratio 1.4 to 29 could be written as 1.4/29 and the ratio 2.8 could be as
2.8/ x where x it he missing number.
Now set up a cross product equation to solve for x.
[tex]\frac{1.4}{29} = \frac{2.8}{x}[/tex] Cross multiply
1.4x = 81.2 Divide both sides by 1.4
x= 58