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]
What’s this I need help with math...
Answer:
3^12 = 531441
Step-by-step explanation:
For this problem, it's important to understand what is meant by the exponents. Notice, there are two sets of separators, a parentheses and a bracket. When you have powers to powers you multiply, hence 2 * 3 * 2 is 12. The given expression can also be broken down like this:
[ ( 3^2 ) ^ 3 ] ^ 2
= [ 3^2 * 3^2 * 3^2 ] ^ 2
= 3^2 * 3^2 * 3^2 * 3^2 * 3^2 * 3^2
And we can apply the rule, when you are multiply powers of like bases you add the exponents. Hence:
3 ^ (2 + 2 + 2 + 2 + 2 + 2)
= 3^12
Either way of power manipulation, you end with the same result of 3^12. Hope this helps.
Cheers.
MATH
Please heeeeeeeeeeeelp
Answer:
3.002 * 10⁵
Step-by-step explanation:
3 * 10⁵ = 3 * 10³ * 10² = 3000 *10²
3 * 10⁵ + 2* 10² = 3000 * 10² + 2*10²
= (3000 + 2) * 10²
= 3002 * 10²
= 3.002 * 10³ * 10²
= 3.002 * 10⁵
Find two consecutive integers whose product is 12.
what’s.the perimeter of a square with an area of 49 cm2
Answer:
28Step-by-step explanation:
Area of a square =
[tex]s^2[/tex]
Perimeter =
[tex]4\times s[/tex]
Where s = side
Solve for s using the area
[tex]A =49\\\\49 = s^2\\\\Square\:root \:both\:sides\:of\:the\:equation\\\\\sqrt{49} = \sqrt{s^2} \\\\7 =s\\\\s =7[/tex]
Find the perimeter
[tex]4\times s\\\\= 4 \times 7\\\\= 28[/tex]
Round 7696.41481885 to the nearest thousand
Round the number 7696.41481885 to the nearest thousandth will be 7696.415.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
The decimal number is the sum of a whole number and part of the fraction number. The fraction number is greater than zero but less than one.
The decimal number is given below.
7696.41481885
Round the number 7696.41481885 to the nearest thousandth term, which will be done if the number is greater than 5 then the previous of that number is increased by 1. Then the number will be
7696.415
Round the number 7696.41481885 to the nearest thousandth will be 7696.415.
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Mount Everest is over 2.9 × 10 4 feet tall. In standard form, that is
Answer:
29000 feet
Step-by-step explanation:
Move decimal points 4 places to the right.
What is the sum? (4x - 3) + (-2x + 5)
Answer:
2x+2
Explanation:
find the square root of each number . if the number is not a perfect square, estimate the squarer root to the nearest integer. 169, 24, 15, 40
Answer:
169 is 13^2
24 is 2(squareroot)6
15 is (squareroot)15
40 is 2(squareroot)10
Step-by-step explanation:
169 is 13^2
24 is 2(squareroot)6
15 is (squareroot)15
40 is 2(squareroot)10
The length of a standard pickleball court is 4 feet more than twice the width. The total perimeter is 128 feet. What are the dimensions of a pickleball court?
Answer:
width= 20
length= 44
Step-by-step explanation:
we can say the width is x and the length is 2x+4 and there are 2 widths and two lengths. so 2x+4+2x+4+x+x=128, 6x+8 = 128 which means x=20 s0 the width is 20 and the length is 44
The length of the pickleball is 44 feet while the width is 20 feet.
What is a rectangle?A rectangle is a geometrical figure in which opposite sides are equal.
The angle between any two consecutive sides will be 90 degrees.
Area of rectangle = length × width.
Perimeter of rectangle = 2( length + width).
Pickleball is a shape of a rectangle.
Let's say the length of the pickleball is L and the width is W
Given that,
The length of a standard pickleball court is 4 feet more than twice the width.
So,
L = 2W + 4
Perimeter 2(L + W) = 128
By substitution,
2(2W + 4 + W) = 128
3W + 4 = 64
W = 20
And L = 2(20) + 4 = 44
Hence "The length of the pickleball is 44 feet while the width is 20 feet".
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In a volcano, erupting lava flows continuously through a tube system about 17 kilometers to the sea. Assume a lava flow speed of 0.5 kilometer per hou calculate how long it takes to reach the sea.
Answer:
Distance = rate x time or d = rt...that means time t = d/r...and we have
t = 21 km / .5 km/hr = 42 hr
Step-by-step explanation:
The amount of time taken by the lava to reach the sea will be 42 hours.
What is speed?Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance. The speed is a scalar quantity it only requires magnitude to represent.
Given In a volcano, erupting lava flows continuously through a tube system about 17 kilometers to the sea. Assume a lava flow speed of 0.5 kilometers per hour.
The distance will be calculated as below:-
Distance = rate x time
d = r x t
t = d / r
t = 21 km / .5 km/hr
t = 42 hr
Therefore, the amount of time taken by the lava to reach the sea will be 42 hours.
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i need alot of help plzzzzzz 50 points and ill give brainliest
Answer:
y=4
y=8
y=12
y=16
2)4=19
5=22
addition of 3 to each value
3)17
4)3a^2
5)a^4
6)1
7)An arithmetic sequence is such that the difference between any term and the one immediately preceeding it is constant.
8)A geometric sequence is such in which each term is a constant multiple of its preceeding.
9)1.25
10)B.
Answer:
y=4
y=8
y=12
y=16
2)4=19
5=22
addition of 3 to each value
3)17
4)3a^2
5)a^4
6)1
7)An arithmetic sequence is such that the difference between any term and the one immediately proceeding it is constant.
8)A geometric sequence is such in which each term is a constant multiple of its proceeding.
9)1.25
10)B.
Step-by-step explanation:
L is the midpoint of KM. If KL = 14x and KM = 26x + 14, what is KL? Simplify your answer and write it as a proper fraction, mixed number, or integer. Please type the answer step by step.
Answer:
Step-by-step explanation:
L is the midpoint of KM. So, length of KL = length of LM
KL = LM = 14x
KL + LM = KM
14x + 14x = 26x + 14 {add the like terms}
28x = 26x + 14 {subtract 26x form both sides}
28x - 26x = 14
2x = 14 {divide both side by 2}
2x/2 = 14/2
x = 7
KL = 14x = 14*7
KL = 98
Question 10 (5 points)
(01.03 LC)
Which of the following is a technology-based way to monitor physical activity? (5 points)
а
Wear a watch.
b
Watch a fitness app strength video.
с
Wear a fitness tracker.
d
Use a scale to record weekly weight totals.
!!!The volume of a cylinder is 675π cm3. The radius of the base of the cylinder is 5 cm. What is the height of the cylinder?
Answer:
The answer is
27 cmStep-by-step explanation:
Volume of a cylinder is given by
V = πr²hwhere
h is the height
r is the radius
V is the volume
Since we are finding the height
[tex]h = \frac{V}{\pi {r}^{2} } [/tex]
From the question
V = 675π cm³
r = 5 cm
Substitute the values into the formula and solve for the height
That's
[tex]h = \frac{675\pi}{ {5}^{2}\pi } \\ = \frac{675\pi}{25\pi} \\ = \frac{675}{25} [/tex]
We have the final answer as
27 cm
Hope this helps you
Simplify completely -3 (4-9) + 6 - 2 (-8 + 5)
What is the most specific name for quadrilateral PQRS? parallelogram rectangle rhombus square
Answer:rhombus
Step-by-step explanation:
Answer:
rhombus
Step-by-step explanation:
A recipe for chili uses 2 cups of beans. Keith is making 1, times the recipe. Which equation helps Keith find how many cups of beans he needs?
Answer:
2x1=2
Step-by-step explanation:
If it asks for 2, but he is making that one time he still needs to use 2.
(10-3x2)2 someone solve this
Answer: 8
(10-3x2)2
(10-6)2
4 x 2
8
Answer:
8
Step-by-step explanation:
3×2=6
10-6=4
4x2=8
Your answer is 8
Solve for x:2/3=x/9 can someone solve this
Hey there!
ANSWER: [tex]x=6[/tex]EXPLANATION:[tex]\frac{2}{3}=\frac{x}{9}[/tex]
For the first step, we will need to use the cross multiplying method.
[tex]\frac{2}{3} =\frac{x}{9}\\ (2)*(9)=(x)*(3)\\18=3x[/tex]
Now let's flip.
[tex]3x=18[/tex]
Now for the final step, we will have to divide both sides by 3.
[tex]\frac{3x}{3} equals\frac{18}{3}[/tex]
Simplify 18/3.
[tex]18/3=6\\6(ANSWER)[/tex]
Hope this helps!
[tex]\text {-TestedHyperr}[/tex]
CAN SOMEONE PLEASE HELP ME !! ^^^^^^
I'll do problem 1 to get you started.
Answers are in bold
1a) Point B. This point is the "hinge" so to speak of the angle 4. Or you can think of the angle as a pair of scissors. Point B is the vertex where the two metal parts meet up.1b) There are two sides to angle 1 and they are BD and BC which form the angle in question. 1c) Angle DBE or Angle EBD are two different ways to relabel angle 5. The order doesn't matter as long as point B is at the center which is where the vertex point is always located.1d) Angle FBC = Either a Right angle or Obtuse angle (it's not clear), Angle EBF = Obtuse angle, Angle ABC = Straight angle1e) Segment EB or BE is an angle bisector. It cuts angle ABD into two equal parts (angle 4 and angle 5 are shown to be congruent through the similar angle markers)1f) Angle EBC = 144 degrees since we simply add the two smaller angle pieces to get the larger angle we want. This works because the two smaller angles are adjacent and form the larger angle.1g) I'm not sure what to do with this one. It seems like info is missing.Plz help me I don't understand the answer!!!!!!!!!!!
what are three ratios equivalent to 8:5
Answer:
80:50 800:500 16:10
Step-by-step explanation:
Use rounding to estimate the product of 198 and 42 . Round both numbers to the nearest ten to find your answer.
Answer:
8000
Step-by-step explanation:
198 and 42 rounded to the nearest hundreths are 200 and 40. the product of 200 and 40 is 8000
The product of 198 and 42 rounded both numbers to the nearest ten
is 8000.
What is rounding off of numbers?We round off numbers to make them easier to remember and it also keeps its value approximately to the place it has been rounded off.
To round off any number to any place we'll look for the digit next to that place and if it is equal to or greater than 5 we'll add one to the previous digit and make all the digits after it zeroes and if the digit is less than 5 we do not add one to the preceding digit and simply make all the digit after it to zeroes.
Given, Use rounding to estimate the product of 198 and 42.
Now, 198 rounded to the nearest ten is 200, and 42 rounded to the nearest ten is 40.
Therefore, The multiplication of 198 and 42 rounded to the nearest 10 is,
= 200×40.
= 8000.
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Deandre downloaded 8 apps onto his tablet in 12 seconds. at this rate, how many apps could be downloaded in one minute?
Answer:
40 apps
Step-by-step explanation:
12 sec ⇒ 8 apps
1 min = 60 sec
therefore, 60 sec ⇒ `60 x 8 / 12 = 40 apps
The table shows three popular flavors according to the results of a survey. What is the
decimal value of those who liked vanilla, chocolate, or strawberry? Round to the
nearest hundredth.
Answer:
0.45
Step-by-step explanation:
4z - 7y + 2 + 2y + 8y + 6z - 15
Answer: 3y + 10z - 13
Step-by-step explanation:
100 points HELP / what is the slope of the line in the graph
A Negative four-thirds
B Negative three-fourths
C Three-fourths
D Four-thirds
Answer:
It is B
Step-by-step explanation:
Find the equation of the line with slope = -8 and passing through (-3,2). Write the equation in point-slope form AND slope-intercept forms. Include the full equation in your answers.
Answer:
Step-by-step explanation:
y - 2 = -8(x + 3)
y - 2 -8x - 24
y = -8x - 22
A survey of 140 pet owners yielded the following information: 47 own fish; 53 own a bird; 50 own a cat; 68 own a dog; 2 own all four; 11 own only fish; 14 own only a bird; 10 own fish and a bird; 21 own fish and a cat; 26 own a bird and a dog; 29 own a cat and a dog; 3 own fish, a bird, a cat, and no dog; 1 owns fish, a bird, a dog, and no cat; 9 own fish, a cat, a dog, and no bird; and 10 own a bird, a cat, a dog, and no fish. How many of the surveyed pet owners have no fish, no birds, no cats, and no dogs? (They own other types of pets.)
Answer:
18
Step-by-step explanation:
This is venn diagram with 4 elements
Fish = n(F)
Bird = n(B)
Dog = n(D)
Cat = n(C)
The formula is given as
n (F ∪ B ∪ C ∪ D) - n(pet owners that have not fish, bird, cat or dogs) = n(F ) + n ( B ) + n (C) + n(D) - n ( F ∩ B) - n ( F ∩ C) - n ( F ∩ D) - n ( D ∩ B) - n ( D ∩ C) - n ( C ∩ B) + n(F ∩ D ∩ C) + n(F ∩ D ∩ B) + n(F ∩ C ∩ B) + n(D ∩ B ∩ C)- n (A ∩ B ∩ C ∩ D)
= 140 - n(pet owners that have not fish, bird, cat or dogs) = 47 + 53 + 50 + 68 - 21 -26 - 29- 10 - 2
140 - n = 218 - 88
140 - 218 - 88 +[(9 + 4 + 10) -(11 + 14)] = n
140 - 218 - 88 + (33 - 25)= n
140 - 130 + 8 = n
10 + 8 = n
Write the recurssive formula. Clarissa is buying a homecoming dress onlayaway. The dress costs $185. She makes a down payment of $20 to put the dress on layaway and then makes weekly payments of $15. In how many weeks will the dress be paid off?
Answer: x = 11
Step-by-step explanation:
185= 15x +20
minus 20 from both side
165 = 15x
divide 15 by both side
11 = x