2. The arithmetic mean of a distribution is 5. The second and the third moments about the mean are 20 and 140 respectively. Find the third moment of the distribution about 10.
Please explain the answer and workings. ​

Answers

Answer 1

Step-by-step explanation:

The arithmetic mean of a distribution is 5. The second and the third moments about the mean are 20 and 140 respectively. What is the third moment of the distribution about 10?

Call the random variable x.

Now, define a new variable y = x - 5. Note that x - 10 = y - 5.

So, it is clear that (x-10)^3 = (y-5)^3

Also, note that (y-5)^3 can be expanded as follows:

Expand (y-5)³

Result ; y³-15 y²+75 y - 125

Letting E denote expectation with respect to the random variable x, we see that

E[(y-5)^3 ] = E(y^3) -15 E(y^2) + 75 E(y) - 125

Again, recalling that y = x - 5, have

E(y^3) = 140

E(y^2) = 20

E(y) = E(x) - 5 = 5 - 5 = 0

Thus,

E[(y-5)^3 ] = 140 -15(20) + 75(0) -125 = -285

Finally, note that

E[(y-5)^3] = E[({x-5} -5)^3] = E[(x-10)^3]

So, we get E[(x-10)^3] = -285.


Related Questions

KBL Ltd. entered into an agreement to lease a vehicle from Morgan Ltd.: Cash price of the vehicle Kshs 20.000 Lease payments: 5 instalments of Kshs 5.142 paid in arrears Required: How much of this finance charge will appear in each year's profit and loss expense in the lessee's books using the actuarial method? (10 Marks)​

Answers

Finance charge is the amount it costs of borrowing money

The finance charge that will appear in each year's profit and loss expense in the lessee's books are;

[tex]\begin{array}{|c|cc|}\mathbf{Year}&&\mathbf{Finance \ Charge \ (Kshs)}\\&&\\First&&1.8\\&&\\Second&&1.499\\&&\\Third&&1.171\\&&\\Fourth&&0.814\\&&\\Fifth&&0.424\end{array}\right][/tex]

The total financial charge = 5 × 5.142 - 20.000 = 5.71

The annual percentage rate, APR, of an instalment payment is given as follows;

[tex]\dfrac{(1 - (1 + r)^{-5}}{r} \times 5.142 = 20.000[/tex]

Solving using a graphing calculator gives;

r = APR ≈ 0.09 = 9%

The calculation for charges each year is as follows:

Payment interest for the first instalment = 20 × 9% = 1.8

The principal of the first payment = 5.142 - 1.8 = 3.342

The loan balance = 20 - 3.342 = 16.658

Payment interest for the second instalment = 16.658 × 9% = 1.49922

Second payment principal = 5.142 - 1.49922 = 3.64278

Loan balance = 16.658 - 3.64278 = 13.01522

Payment interest for the third instalment = 13.01522 × 9% = 1.1713698

Third payment principal = 5.142 - 1.1713698 = 3.9706302

Loan balance = 13.01522 - 3.9706302 = 9.0445898

Interest for the fourth payment = 9.0445898 × 9% = 0.814013082

Fourth payment principal = 5.142 - 0.814013082 ≈ 4.327986918

Loan balance = 9.0445898 - 4.327986918 = 4.716602882

Fifth payment interest = 4.716602882 × 9% = 0.42449425938

Fifth payment principal = 5.142 - 0.42449425938 ≈ 4.718

Therefore, we have;

[tex]\begin{array}{|c|cc|}\mathbf{Year}&&\mathbf{Finance \ Charge \ (Kshs)}\\&&\\First&&1.8\\&&\\Second&&1.499\\&&\\Third&&1.171\\&&\\Fourth&&0.814\\&&\\Fifth&&0.424\end{array}\right][/tex]

Learn more about the actuarial method here:

https://brainly.com/question/15504405

A kite is inscribed in a rectangle. Everything outside of the kite is shaded. The points of the kite split the lengths of the rectangle into a length of 3x and x. The points of the kite split the height of the rectangle into lengths of x and x. The total length of the rectangle is 4 x and the height is 2 x.
The figure shows a kite inside a rectangle. Which expression represents the area of the shaded region?

2x2
4x2
6x2
8x2

Answers

Answer:

B

Step-by-step explanation:

you can make picture into to shapes. a rectangle and a square. the square would be x2 and the rectangle would be 3x2. just add them together while your answer would be 4x2. doing this assignment right now so best of luck.

Answer:

b

Step-by-step explanation:

i just did the test

Which of the following is equivalent to?

Answers

Answer:

[tex]5 \sqrt{ {13}^{3} } = {13}^{ \frac{3}{5} } [/tex]

The center circle on a soccer field has a radius of 9 yards. What is the area of the center circle? Use 3.14 for pie

Answers

Answer:

[tex]\boxed {\boxed {\sf 254.34 \ yd^2}}[/tex]

Step-by-step explanation:

The area of a shape is the space occupied by the surface of an object. The area of a circle can be calculated using the following formula.

[tex]a= \pi r^2[/tex]

The radius (r) of the center circle on the soccer field is 9 yards. We are asked to use 3.14 for pi.

r= 9 yd π= 3.14

Substitute these values into the formula.

[tex]a= (3.14)(9 \ yd)^2[/tex]

Solve the exponent.

(9 yd)² = 9 yd * 9 yd = 81 yd²

[tex]a= (3.14)(81 \ yd^2)[/tex]

Multiply.

[tex]a= 254.34 \ yd^2[/tex]

The area of the center circle on the soccer field is 254.34 square yards.

A 16-ft steel beam is to be cut into two pieces so
that one piece is 1 foot longer than twice the other.
Find the length of each piece.

Answers

Answer:

8.5 feet and 7.5 feet.

Step-by-step explanation:

Hope this helps :)

Thx god bless stay safe

Answers

Answer and Step-by-step explanation:

The answer is qualitive because the phrase is describing outside to being cold.

#teamtrees #PAW (Plant And Water)

Answer: Qualitative

Please mark brainliest

The arithmetic sequence a; is defined by the formula: a1=4 +3(i-1)

Answers

Answer:

the arithmetic sequence ai is defined by the formula: a1= 2 ai= ai - 1 -3 find the sum of the first 335 terms in the sequence. 1.

How do you solve by undoing for 4-2x-x=12 in Algebra 1​

Answers

Hi ;-)

[tex]4-2x-x=12\\\\-2x-x=12-4\\\\-3x=8 \ \ /:(-3)\\\\x=-\frac{8}{3}=-2\frac{1}{3}[/tex]

Rachael made 4 pounds of potato salad. How many ounces of potato salad did Rachael make?

Answers

Answer:

i think the answer is 64 ounces

is 9.407 a rational number?

Answers

Answer:

Yes, sure!

Step-by-step explanation:

I said ''Yes, sure.'' Because We number 9.407 is a decimal number, and decimals are always rational numbers.

9.407= 9407/1000

Answer

yes

Step-by-step explanation:

all numbers that have decimal places and are fractions are rational

please mark me the Brainiest

Please help! I don’t know the answer to this.

Answers

Answer:

as we can see b and are reflections as ther are same

what percentage is 10 in 24? ​

Answers

Answer:

41.67

Step-by-step explanation:

10: 24×100 =

(10×100): 24 =

1000: 24 = 41.67

41.67 is the answer I’m not sure

Ali has 126 marbles. He has 3 times as many marbles as ravi. Janice has 20 marbles more than ravi.
a) How many marbles does janice have?
b) How many marbles do they have altogether?

Answers

Answer:

a) 62

Step-by-step explanation:

126=(Ali)

126÷3=42(ravi)

42+20=62(janice)

b) 126+42+62= 230marbles

Create a function that generates for any value x the corresponding value y when
y= 17x^2+ 14x +9

Required:
What is the value y when x =12?

Answers

Answer:

Step-by-step explanation:

JT has two jobs. He mows yards and washes cars in his neighborhood. Let X represent the amount of weekly
earnings for mowing yards, and let y represent the amount of weekly earnings for washing cars. The mean of X is
$60, and the mean of Y is $35. Which answer choice correctly calculates and interprets the mean of the sum, S= X
+ Y?
Ps = 47.5; next week, JT will earn $47.5.
Hs = 47.5; JT can expect to earn $47.5, on average, in a typical week.
Hs = 95; next week, JT will earn $95.
Ps = 95: JT can expect to earn $95, on average, in a typical week.

Answers

The answer is 95, because x=60 and y=35 then S=60+35=95

Answer is D) 95; JT can expect blah blahh

round decimal to the nearest whole number.
12.1

Answers

Answer:

12

Step-by-step explanation:

12.1 to the nearest whole number is 12.

Answer:

12

Step-by-step explanation:

12.1 there is no number behind the one, therefore it becomes 12

If f(x) =2x - 3, find the following

1. f(-2)
2. f(7)
3. f(-4)

Answers

Answer:

1. f(-2) = -7

2.f(7) = 11

3. f(-4) = -11

Step-by-step explanation:

1. substitute x = -2 in f(x)

The function becomes :

f(-2) = 2×(-2) - 3 = -7

2. substitute x = 7 in f(x)

the function becomes:

f(7)= 2×7 - 3 = 11

Can you explain what a stem and leaf plot is?

Answers

Answer:

A stem and leaf plot, or stem plot, is a technique used to classify either discrete or continuous variables. A stem and leaf plot is used to organize data as they are collected. ... Each number in the data is broken down into a stem and a leaf, thus the name. The stem of the number includes all but the last digit

hope it helped!

what is the equation of the function y= 3/x translated 2 units to the left and seven units up

Answers

Answer:

y = (3/x + 2) + 7

Step-by-step explanation:

The additive inside the parenthesis moves the function to the left (adding moves left, subtracting moves right) and the additive outside moves the function up (adding moves up, subtracting moves down).

if the cost price of 10 tables is equal to the selling price of 16 tables , find out the gain or loss percentage​

Answers

Hi,

To solve this problem, Let us take the LCM of 10 and 16 which will come 80.

Now suppose the cost price of 10 tables =₹n CP of 80 tables will be ₹ 8n

According to the question, CP of 10 tables is equal to the SP of 16 tables, then

the SP of 16 tables will also be ₹ n.

So, SP of 80 tables will be ₹ 5n

So, Loss = CP-SP

→ 8n - 5n = ₹ 3n

Loss%= (3n×100)/8n

Loss%= 37.5%.

Hence the correct answer will be a loss of 37.5%.

Which expression has a value that is 6 times the value of the expression 63 - 3y?
ОА. 6x 63 – Зу
O B. 63 – 3y = 6
Ос. 63 = (6 x Зу)
OD. 6 X (63 – 3y)

Answers

D. i just took the quiz

Jungwon has $15. Notepads cost $2.50 each. How many notepads can Jungwon buy?​

Answers

15 divided by 2.50 is 6
So Jungwon has $15 and each notepad costs $2.50. We need to find out how many notepads Jungwon can buy with $15. Simply take $15 and divide that by $2.50, you get 6. Jungwon can buy 6 notepads with $15.

Determine a series of transformation that would map figure h onto Figure I

Answers

Answer:

isnt it figure h???

Step-by-step explanation:

Answer:

A translation right 8 units followed by a reflection over the x-axis

Step-by-step explanation:

Find the slope of the line through each pair of points.
(2,-9),(-1,4)

Answers

(2,9)(-1,4)

[tex]\\ \rm\hookrightarrow Slope=m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\\ \rm\hookrightarrow m=\dfrac{4-9}{-1-2}[/tex]

[tex]\\ \rm\hookrightarrow m=\dfrac{-5}{-3}[/tex]

[tex]\\ \rm\hookrightarrow m=\dfrac{5}{3}[/tex]

Answer:

-13/3

Step-by-step explanation:

The formula for slope is [ y2-y1/x2-x1 ].

4-(-9)/-1-2

13/-3

-13/3

Best of Luck!

2x-3y=-1
y=x-1

solve. systems of equations

Answers

Answer:

x=4

y=3​

Step-by-step explanation:

Will give brainly est
Find the difference. Enter your answer in simplest form.

3 1/3 minus 2 5/12 The First 3 and the first two are whole numbers btw


options

1 4/9 A

11/12 B

7/12 C

1 1/2 D

Answers

[tex]\\ \sf\longmapsto 3\dfrac{1}{3}-2\dfrac{5}{12}[/tex]

[tex]\\ \sf\longmapsto \dfrac{10}{3}-\dfrac{29}{12}[/tex]

[tex]\\ \sf\longmapsto \dfrac{40-29}{12}[/tex]

[tex]\\ \sf\longmapsto \dfrac{11}{12}[/tex]

what does the answer on her sceen mean?

Answers

Answer:

Ahhh!! am not seeing the answer on the sceen.

Please help its due today will give 15+ points and make brainlyiest

Answers

absolute value of -3

hope it helped

What is a 15 of the sequence –7,2, 11, ...?

Answers

We can see: Everytime, the new number is the sum of the number behind it with 9.

So the 15th will total add: 9 x 14 = 126

Start from number -7 so the 15th number is : 126 -7 = 119

SO: B.119 is the answer

NL: Sorry my english was bad

Answer:

119

Step-by-step explanation:

We need to find the 15th term in the sequence. The pattern is that each term increases by 9.

We can then count to the 15th term

-7 + 14*9 = 119

Therefore, the 15th term is equal to 119, or answer B.

How many area codes (ABC) would be possible if all three digits could be any value 3-9

Answers

Answer:

Step-by-step explanation:

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