The maximum likelihood estimate of θ for the given data is 1/3.
The likelihood function L(θ|x) for a sample of n observations x1, x2, ..., xn from a Pareto distribution with parameter θ is given by:
L(θ|x) = f(x1|θ) × f(x2|θ) × ... × f(xn|θ)
where f(xi|θ) is the probability density function of the Pareto distribution with parameter θ evaluated at xi.
Substituting the given pdf of the Pareto distribution with parameter 0, we get:
L(θ|x) = (θ/5θ) × (θ/10θ) × (θ/8θ) = θ³ / 4000
Taking the natural logarithm of the likelihood function, we get:
ln L(θ|x) = 3 ln θ - ln 4000
To find the maximum likelihood estimate (MLE) of θ, we differentiate ln L(θ|x) with respect to θ and set the derivative equal to zero:
d/dθ ln L(θ|x) = 3/θ = 0
Solving for θ, we get:
θ = 1/3
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The maximum likelihood estimate of θ for the given data is 0.501
Calculating the maximum likelihood of θFrom the question, we have the following parameters that can be used in our computation:
[tex]f(x|\theta) = \frac{\theta}{x^{\theta+ 1} }[/tex]
The likelihood function L(θ|x) for a Pareto distribution with parameter θ is calculated using
L(θ|x) = f(x₁|θ) * f(x₂|θ) * .....
Recall that
[tex]f(x|\theta) = \frac{\theta}{x^{\theta+ 1} }[/tex]
And
θ = 5, 10, 8
So, we have
[tex]L(\theta|x) = \frac{\theta}{5^{\theta+ 1} } * \frac{\theta}{8^{\theta+ 1} } * \frac{\theta}{10^{\theta+ 1} }[/tex]
Taking the natural logarithm both sides
[tex]\ln(L(\theta|x)) = \ln(\frac{\theta}{5^{\theta+ 1} } * \frac{\theta}{8^{\theta+ 1} } * \frac{\theta}{10^{\theta+ 1} })[/tex]
Differentiate
ln L'(θ|x) = -[(ln(10) + ln(8) + ln(5))θ - 3]/θ
Set the differentiated equation to 0
So, we have
-[(ln(10) + ln(8) + ln(5))θ - 3]/θ = 0
Solve for θ, we get:
(ln(10) + ln(8) + ln(5))θ = 3
So, we have
θ = 3/(ln(10) + ln(8) + ln(5))
Evaluate
θ = 0.501
Hence, the maximum likelihood of θ is 0.501
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The hypotenuse of a right triangle measures 15 cm and one of its legs
measures 5 cm. Find the measure of the other leg. If necessary, round to the
nearest tenth.
Answer:
[see below]
Step-by-step explanation:
Use the Pythagorean Theorem.
[tex]a^2+b^2=c^2[/tex]
'c' will be the hypotenuse.
The hypotenuse is 15 cm. One of the legs is 5 cm.
[tex]5^2+b^2=15^2\\\\25 + b^2 = 225\\\\25-25+b^2=225-25\\\\b^2=200\\\\\sqrt{b^2}=\sqrt{200}\\\\ b=14.1421356237..., -14.1421356237[/tex]
14.1421356237 ≈ 14.1
The other leg should be about 14.1 cm.
Hope this helps.
The length of the other leg is 14.14 cm rounded to two decimal places.
What is Pythagoras's theorem?In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.
Given, The hypotenuse of a right triangle measures 15 cm, and one of its legs measures 5 cm.
We know,
Hypotenuse² = Base² + Adjacent².
Therefore,
15² = 5² + Adjacent².
Adjacent = √(225 - 25).
Adjacent = √200.
Adjacent = 14.14.
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Elias swam 1,170 laps in the pool last week. If he
spent a total of 6 hours swimming laps, how
many laps per minute did he average?
6 hrs x 60 min = 360 min
1170/360=3.25 laps/min
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Which figure has no line of symmetry
Answer:
the first figure
Step-by-step explanation:
PLEASE HELP ME!!!!!!!!!!!!
Rosa is selling juice and cookies for a fundraiser. She earns $2 for every cookie and $3 for every bottle of juice. She wants to earn at least $24 from all the sales. Let x represent the number of cookies sold and y represent the number of bottles of juice sold. What does the slope of this inequality represent? 2x + 3y ≥ 24
Answer:
The slope is 2. It represents the price of the cookies.
Step-by-step explanation:
The slope is 2 because its in frount of the x and 2 is the price of the cookies.
Gambarlah sebuah lingkaran dengan jari jari 2,5 cm. Lalu gambarlah 3 buah sudut keliling yg menghadap busur yang sama
Step-by-step explanation:
isidhxibdofeixeosgzifisvsoshzibdihddgd
Do you know anything about y=mx+b
Answer:
yes
Step-by-step explanation:
your m is your slope,your b is the y-intercept, and your y is what you are solving for.
Answer:
Y=mx+b is an equation for a linear equation
M is the slope of the line and B is the y-intercept
The y-intercept of this line is the value of y at the point where the line crosses the y axis.
Every straight line can be represented by an equation: y = mx + b.
Hope this helps :))
Find the value of x when the triangle has 9 and 3
Answer:
H²=h²+b²
H²=9²+3²
H²=81+9
H²=90
H=
[tex] \sqrt{90} [/tex]
Every year Ethan ears 38,428. Every year he spends 21,728 on expenses. How much money should Ethan have leftover?
Answer:
16,700
Step-by-step explanation:
38,428
_
21,728
=
16,700
Work out the sum of 1/6 , 4/5 and 2/3 Give your answer as a mixed number in its simplest form.
Answer:
39/30= 13/10
Step-by-step explanation:
You would need to make all numbers have a common denominator. The least common denominator for them is 30. So multiply the 1/6 by 5. the 4/5 by 6 and the 2/3 by 10. And the answer will come out to be a mixed number.
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Answer:
B
Step-by-step explanation:
did the math for it!!
B, jake.
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Combine the like terms to create an equivalent expression:2r+1+(−4r)+7
Answer:
2r+1+(-4r)+7
= -2r+8
= -2(r+4)
Step-by-step explanation:
Madison was working at a store in the mall. She earns 7% commission for each sale that she makes. Last month, she sold a total of $1,450. How much commission did she earn?
Answer:
101.50
Step-by-step explanation:
Answer:
$101.50
Step-by-step explanation:
7% of 1450 = 0.07 × 1450 = 101.5
Plz help me!!
Can someone tell me how to get the answer as well plz? Thank you
Proving trapezoid theorems Geometry
Answer:
ΔABD ≅ ΔACD by SAS, therefore;
[tex]\overline {BD} \cong \overline {CA}[/tex] by CPCTC
Step-by-step explanation:
The two column proof is presented as follows;
Statement [tex]{}[/tex] Reason
ABCD is a trapezoid [tex]{}[/tex] Given
[tex]\overline {BA} \cong \overline {CD}[/tex] [tex]{}[/tex] Given
[tex]\overline {BC} \parallel \overline {AD}[/tex] [tex]{}[/tex] Definition of a trapezoid
ABCD is an isosceles trapezoid [tex]{}[/tex] Left and right leg are equal
∠BAD ≅ ∠CDA [tex]{}[/tex] Base angle of an isosceles trapezoid are congruent
[tex]\overline {AD} \cong \overline {AD}[/tex] [tex]{}[/tex] Reflexive property
ΔABD ≅ ΔACD [tex]{}[/tex] By SAS rule of congruency
[tex]\overline {BD} \cong \overline {CA}[/tex] [tex]{}[/tex] CPCTC
CPCTC; Congruent Parts of Congruent Triangles are Congruent
SAS; Side Angle Side rule of congruency
Answer:
Step-by-step explanation:
just did it
I don’t know if this is correct !!!!! Please help answer correctly !!!!!!!!! Will mark Brianliest !!!!!!!!!!!
Answer:
change up to down the rest is right
Step-by-step explanation:
hope I helped!!
STATE 2 DECIMALS BETWEEN 2.10 AND 2.11 Please help!
Answer:
There are many decimals between 2.10 and 2.11.
Examples:
2.101, 2.102, 2.103, 2.104, 2.105, 2.106, 2.107, 2.108, 2.109
You can choose 2 from these examples.
holly has 368 pet pal cards Dara has 243 cards how much more does holly have then Dara
Answer:
125
Step-by-step explanation:
Answer:
125
Step-by-step explanation:
368 - 243 = 125
What is the y-intercept
Step-by-step explanation:
To find the y intercept we need to find slope first which can be done by taking 2 points and using the slope formula
5 - 10
---------- = -5/3
12--9
The slope is -5/3 now we take one point substitute the slope in and find the y intercept
5=-12( -5/3) +b
5= 20+ b
-15 =b
The y-intercept is -15
Jane made a poster that had a length of 1 2/3 feet and a width of 5/6 feet. What is the perimeter of her poster?
answers; 1 7/18, 2 1/2, 3 feet, and 5 feet.
Answer:
5 feet
Step-by-step explanation:
You can upgrade lighting at your factory to LED bulbs that coast 6.95 each and last an average of 5 years.
Answer:
$200
Step-by-step explanation:
Here is the full question
You can upgrade lighting at your factory to LED bulbs that cost $6.95 each and last an average of 5 years. It costs $3 in labor to change a bulb. Over a 10-year period, about how much will it cost per year to install LED bulbs in 100 lamps and change the bulbs when they burn out?
in 10 years, the bulbs would be changed twice
Total cost incurred per bulb in 10 years = (6.95 + $3) x 2 = $19.90
Since there are 100 bulbs, total cost incurred would be - $19.90 x 100 = $1990
Cost per year = $1990 / (6.95 + $3) = $200
Rahul sold a painting at 10% profit. If he had sold it for 240 more, he would have made 15% profit. What is the C.P. of the painting?
please tell ans step by step..
Answer:
$4800
Step-by-step explanation:
Let x be the C.P of the painting.
Profit=10% of x
Profit=[tex]\frac{10}{100}\times x=\frac{10x}{100}[/tex]
If S.P increase by 240 then
Profit=15% of x=[tex]\frac{15x}{100}[/tex]
For first case
S.P=C.P+ Profit
S.P=x+10x/100
S.P=[tex]\frac{100x+10x}{100}=\frac{110}{100}x[/tex]
For second case
New S.P[tex]=x+\frac{15}{100}x[/tex]
=[tex]\frac{115}{100}x[/tex]
According to question
[tex]240+S.P=\frac{115}{100}x[/tex]
[tex]240+\frac{110x}{100}=\frac{115}{100}x[/tex]
[tex]240=\frac{115}{100}x-\frac{110x}{100}[/tex]
[tex]240=\frac{115x-110x}{100}[/tex]
[tex]240=\frac{5}{100}x[/tex]
[tex]x=\frac{240\times 100}{5}[/tex]
[tex]x=4800[/tex]
Hence, the C.P of the painting=$4800
Is this a, b, c, or d?
Answer:
Alright so let's start by elimination.
Step-by-step explanation:
It cannot be 1/4 (unless it's y or x)
Cannot be 1/2 unless it's the bottom part.
So that leaves you with 1/3 and 1/6, 1/6 is to small so it has to be 1/3.
Hope this helps!
Find the measure of each angle in the angle pair described.
The measure of one angle is twice the measure of its supplement. What are the measures of the two angles?
Answer:
The best way to measure an angle is to use a protractor. To do this, you'll start by lining up one ray along the 0-degree line on the protractor. Then, line up the vertex with the midpoint of the protractor. Follow the second ray to determine the angle's measurement to the nearest degree
At the student store, pencils are sold in either packs of three or packs of eight.
Without opening any packages, which numbers of pencils is it possible to buy?
Which numbers are impossible?
Answer
4, 7, 5, 10, 13, .......
Step-by-step explanation:
the only numbers that are impossible to get are the non-multiples of 3 and 8
and the numbers that 8 and 3 do not add up to and the multiples of 8 and 3 do not add up to
Which of these graphs represents a function?
-5-4-3-2-1, 1 2 3 4 5
-5-4-3-2-11
-5
-5
w.
X.
.4-3-2-1,
1 2 3
5-4-3-2-13
1 2 3 4 5
.51
Y.
Since each value of the input is mapped to only one value of the output, we have that graph w represents a function.
When does a graph represents a function?When it has no vertically aligned points, that is, each value of x is mapped to only one value of y.
Hence, in this problem, graph w represents a function.
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Answer:
it's A have a good day
Step-by-step explanation:
help again i need help
Answer:
2.25
Step-by-step explanation:
32 divided by 14 2/9
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Helppppppppp me plz I rlly. We’d help
Answer:
c = 4,9
d = 4,6
PLEASE HELP! WILL MARK BRAINLIEST IF U ANSWER CORRECTLY! IF WRONG U WONT GET IT
Answer:
1120 super easy
Step-by-step explanation:
8x10=80
80x14=1120
What is the value of x in the matrix equation below?
=======================================================
Explanation:
The -2 outside the first matrix multiplies to every item inside that first matrix.
So the x updates to -2x in the upper left corner.
That -2x adds to the 3 in the upper left corner of the second matrix. The sum -2x+3 must be equal to the value in the upper left corner of the third matrix.
Everything is focused on the upper left corner.
So we must solve -2x+3 = x
Doing so leads to...
-2x+3 = x
3 = x+2x
3 = 3x
3x = 3
x = 3/3
x = 1
Helpppppppp pls help .
Answer: X= 1 2 3 4 Y= 5 8 11 14
Step-by-step explanation: i tried my best