Defined the total variation distance to be a distance TV(P,Q) between two probability measures P and Q. However, we will also refer to the total variation distance between two random variables or between two pdfs or two pmfs, as in the following.

Compute TV(X,X+a) for any a∈(0,1), where X∼Ber(0.5).

TV(X,X+a) = ?

Answers

Answer 1

Answer:

1

Step-by-step explanation:

Computing Tv(X, X + a ) for any a∈(0,1)

Given that :  X∼Ber(0.5)

∴ The probability mass function

    P(X = 1 ) = 0.5

    P(X = 0) = ( 1 - 0.5 )

and expectation  E[X] = 0.5

hence ; TV ( X, X + a ) = 1


Related Questions

Plsss help pls...........

Answers

Answer: Prime numbers are divisible by themselves ONLY. 11 is a prime number but 8 isn't because it can be divided by both 2 and 4.

Step-by-step explanation:

11 + 2 + 4 + 6 = 23

23 is prime number every time...

I hope you understand...

The Coffee Counter charges ​$8.00 per pound for Kenyan French Roast coffee and ​$10.00 per pound for Sumatran coffee. How much of each type should be used to make an 18 pound blend that sells for ​$9.00 per​ pound?
The Coffee Counter should mix ___ pounds of Kenyan Roast coffee and ___ pounds of Sumatran coffee to make 18 pounds of a blend that sells for ​$9.00 per pound.

Answers

Answer:

x = 9

y = 9

Step-by-step explanation:

Given :

Let :

Kenyan French roast coffee = x

Cost per x = $8

Sumatran Coffee = y

Cost per y = $10

x + y = 18 - - - - (1)

8x + 10y = 9 * 18 ;

8x + 10y = 162 - - - - (2)

From (1):

x = 18 - y

Put x = 18 - y in (2)

8(18 - y) + 10y = 162

144 - 8y + 10y = 162

2y = 162 - 144

2y = 18

y = 9

x = 18 - y

x = 18 - 9

x = 9

Consider the line that passes through the point P(4, - 2) and is parallel to the line - 3x - 4y = 2 Write the point-slope equation of the line. Use exact values.

Answers

9514 1404 393

Answer:

  y +2 = -3/4(x -4)

Step-by-step explanation:

A line parallel to ...

  ax +by = c

through point (h, k) can have the equation ...

  a(x -h) +b(y -k) = 0

It is pretty simple to put this into point-slope form:

  b(y -k) = -a(x -h) . . . . . subtract the x-term

  y -k = (-a/b)(x -h) . . . . divide by b

__

We have ...

  a = -3, b = -4, (h, k) = (4, -2)

so the point-slope form equation is ...

  y -(-2) = (-(-3)/(-4))(x -4)

  y +2 = -3/4(x -4)

With the growth of internet service providers, a researcher decides to examine whether there is a correlation between cost of internet service per month and degree of customer satisfaction (higher scores mean high satisfaction). The researcher only includes programs with comparable types of services. Calculate the Pearson's correlation coefficient for the dataset below and interpret what that means.

Answers

Answer:

The correlation is 0.373 . There is a moderate positive linear association between Dollars and Satisfaction.

Step-by-step explanation:

Given the data:

Dollars Satisfaction

70.99 32

76.01 34

67.24 27

69.33 17

67.59 23

74.06 29

76.04 25

72.63 31

68.01 26

67.98 31

Using technology, the Pearson correlation Coefficient calculator ; we can obtain the Pearson correlation Coefficient is 0.3729

Interpretating this value, a correlation Coefficient value of 0.3729 is positive, this means a positive linear relationship exists between the values. Also 0.3729 is closer to 0 than 1 ; this mean that the strength of their relationship is moderate to weak .

Hence, a correlation Coefficient value of 0.3729 means that a weak positive relationship exists between dollar and satisfaction

Jennifer’s pie shop recorded how many pies it recently sold in each flavor. Lemon meringue pies 2 apple pies 3 peach pies 2 blueberry pies 4 coconut cream pies 1 considering this data, how many of the next 15 pies sold should you expect to be blueberry pies?

Answers

Answer:

correct me if im wrong but im assuming four just cause if you count what you have all ready not couting the 15 pies. You have at leat 12 and not couting the lemon pies. And from there you basically have to just thing and do the math and I got at least 3 to 5 pies that should be blueberry. srry for my spekling it ducks

We can expect that out of the next 15 pies sold, approximately 5 of them will be blueberry pies.

What is a relative frequency?

Relative frequency is a statistical measure that expresses the proportion or percentage of times an event occurs in relation to the total number of events.

We have,

To estimate how many of the next 15 pies sold should be blueberry pies, we can use the relative frequency of blueberry pies in the given data.

The relative frequency of a pie flavor is the ratio of the number of pies of that flavor to the total number of pies.

The total number of pies sold in this data is:

= 2 + 3 + 2 + 4 + 1

= 12

The number of blueberry pies sold is 4.

The relative frequency of blueberry pies.

= 4/12

= 1/3

This means that 1/3 of the pies sold were blueberry pies.

To estimate the number of blueberry pies out of the next 15 pies sold, we can multiply 15 by the relative frequency of blueberry pies.

= 15 x (1/3)

= 5

Therefore,

We can expect that out of the next 15 pies sold, approximately 5 of them will be blueberry pies.

Learn more about relative frequency here:

https://brainly.com/question/29739263

#SPJ2

Determine whether the following equation defines y as a function of x.
x + y = 27
Does the equation x + y = 27 define y as a function of x?
O Yes
Ο Νο

Answers

Answer:

The equation can define y as a function of x and it also can define x as a function of y.

Step-by-step explanation:

A relation is a function if and only if each value in the domain is mapped into only one value in the range.

So, if we have:

f(x₀) = A

and, for the same input x₀:

f(x₀) = B

Then this is not a function, because it is mapping the element x₀ into two different outputs.

Now we want to see it:

x + y = 27

defines y as a function of x.

if we isolate y, we get:

y = f(x) = 27 - x

Now, this is a linear equation, so for each value of x we will find an unique correspondent value of y, so yes, this is a function.

Now we also want to check if:

x +  y = 27

defines x as a function of y.

So now we need to isolate x to get:

x = f(y) = 27 - y

Again, this is a linear equation, there are no values of y such that f(y) has two different values. Then this is a function.

if 100% = Rs 120,then. A.120% = Rs 84 B. 20% = Rs 84 C. 70% = Rs 84 D. 30% = Rs 84​

Answers

Answer:

70% is Rs 84

just use the formula

x% of 120= 84

and you will get the answer

One bag of marbles contains 2 black , 3 red , and 5 white marbles . A second bag contains 3 white and 2 black marbles . What is the probability of selecting one marble from each bag and that they are not both black.
Please help!!

Answers

Answer:

NOT BOTH BLACK = 1-2/25 = 23/25

Step-by-step explanation:

Bag 1 : 8 non-black out of 10

P(1) = 8/10

Bag 2: 3 non-black out of 10

P(2)=3/5

Probability of both independent events happening can be calculated using the multiplication rule

P(1) and P(2) = P(1)*P(2) = 8/10 * 3/5 = 24/50 = 12/25 (both are not black, or none is black)

Interpretating not both black meaning at most one black, then

we calculate the probability of both are black,

P(1) = 2/10

P(2) = 2/5

Probability that both balls are black can be calculated using the multiplication rule

P(1) and P(2) = 2/10 * 2/5 = 2/25

Probability that NOT BOTH BLACK = 1-2/25 = 23/25, i.e. at most one black

Tiffany is borrowing 1,200 from her parents to buy a new laptop computer. She plans to pay them back at the rate of $70 a month. Rosie is borrowing $900 from her parents to buy a violin. She plans to pay her parents back at the rate of $40 per month

Answers

This isn't really a question so I'll just go through all of it.

1200 dollars will take about 17 months to pay off with installments of 70 dollars.

900 dollars will take 22.5 months to pay off with 40 dollar installments.

Tiffany will pay off her debt first.

I can not figure out word problems, please help.
The area of a rectangle is 29 square feet. If the length is 3 times the width, then find the dimensions of the rectangle. Round off your answers to the nearest hundredth.

Answers

Step-by-step explanation:

a rectangle which has a length which was three times the width could be

3 x 9 - this would give a total of just 27 feet.....so we know its bigger than this.....but essentially this starting place puts us in the right ballpark

following on from this....

if we do.....3.11 x 9.33 - this gives us 29.0163

and we have a rectangle which meets the criteria

four times a certain number decreased by twice the same number gives 17. the number is​

Answers

Answer:

8.5

Step-by-step explanation:

Pineapples are sold at 'd' cents per pound. The total weight of 3 pineapples
is 5 pounds. What is the average cost of 1 pineapple?

Answers

Answer:

(5/3)d cents    exact

1.67d cents     decimal approximation

Step-by-step explanation:

Average weight

5pounds/3pineapples = (5/3) pounds/pineapple

Cost of 1 pineapple

(5/3) pounds * dcents/pound

(5/3)d cents    exact

1.67d cents     decimal approximation

The diameter of a £1 coin is 22.5 mm. Work out its circumference to the nearest centimetre.Required to answer. Single choice.
(2 Points)
68
70
7
11

Answers

Answer:

7

Step-by-step explanation:

Circunference:

The circunference of a circle with diameter d is given by:

[tex]C = d\pi[/tex]

The diameter of a £1 coin is 22.5 mm.

Each mm has 0.1 cm, so the diameter, in cm, is of d = 2.25. Then

[tex]C = 2.25\pi = 7[/tex]

The circunference is of 7 centimeters.

*PLEASE HELP ASAP I WILL MARK BRAINLIST*
(Questions and Answers pictured)

Answers

Answer:

The first equation, sorry can’t explain.

Answer:

g(x)=3f(2x)

I think

Consider the given functions. Select the expression that will produce h(x). A. f(x) + f(x) B. f(x) − g(x) C. f(x) + g(x) D. g(x) − f(x)

Answers

Answer:

here is your answer

Step-by-step explanation:

here is your answer

5
21. The average of 5 consecutive integers starting with m
as the first integer is n. What is the average of 9
consecutive integers that start with m+2?
A) m + 4
B) n + 6
C) n+ 4
D) m + 5

Answers

Answer:

n + 4

Step-by-step explanation:

Given

⅕(m + m + 1 + m + 2 + m + 3 + m + 4) = n

Required

⅑(m + 2 + m + 3 +.......+ m + 10)

We have:

⅕(m + m + 1 + m + 2 + m + 3 + m + 4) = n

Multiply both sides by 5

m + m + 1 + m + 2 + m + 3 + m + 4 = 5n

Collect like terms

m + m + m + m + m = 5n - 1 - 2 - 3 - 4

5m = 5n - 10

Divide both sides by 5

m = n - 2

So, we have:

⅑(m + 2 + m + 3 + m + 4 + m + 5 + m + 6 + m + 7 + m + 8 + m + 9 + m + 10)

Collect like terms

= ⅑(m+m+m+m+m+m+m+m+m+2+3+4+5+6+7+8+9+10)

= ⅑(9m + 54)

= m + 6

Substitute n - 2 for m

= n - 2 + 6

= n + 4

Can somebody help me out please

Answers

Answer:

Brainly's honor code doesn't allow quiz questions to be posted.

"Students are never allowed 2 post questions directly from tests, quizzes, and assessments, or copy answers found on Brainly during tests, quizzes, and assessments."

Which matrix represents the system of equations shown below?
2x - 5y = 4
-5y = 8
c
D
А
B
2 -547 2x -5y 47 52-547
-5 08 0 -5y8 0 -58
2 041
-5 -5 8
A. Matrix A
B. Matrix B
C. Matrix C
D. Matrix D

Answers

9514 1404 393

Answer:

  C.  Matrix C

Step-by-step explanation:

The usual form for an augmented matrix representation of a system of linear equations has the variable coefficients listed in a square matrix with an additional column at the right containing the constants in the standard-form equations. This is illustrated in Matrix C.

__

The variables in the equations are usually left out of the matrix. That is, the system of equations AX= B is usually represented by the augmented matrix A|B, rather than (AX)|B. Thus "Matrix B" is not the best choice.

Someone please help with the questions on this picture!! URGENT!!!

Answers

Answer:

A) Independent

B) Dependent

Step-by-step explanation:

A) If we take a marble out and put the marble back, it means we have restored the sample to what it was initially and thus it doesn't affect probability of making another selection.

Thus, this is an independent event.

B) A card is taken from a deck of cards without replacement and set aside. Then after that another card is taken from the first sample, this means that the first sample size has now reduced and thus the first card taken affects the probability of the second card to be picked. Thus, this is a dependent event.

Roulette is a casino game that involves spinning a ball on a wheel that is marked with numbered squares that are red, black, or green. Half of the numbers 1 - 36 are colored red and half are black and the numbers 0 and 00 are green. Each number occurs only once on the wheel. What is the probability of landing on a red space?​

Answers

Answer:

18/38 or 9/19

Step-by-step explanation:

18 squares are red

18 squares are black

2 squares have 0 or 00

The ratio of girls to boys in a particular classroom is 8: 7. How many boys are in the class if there are 45 students?

Answers

Answer:

8+6=14

So , we can multiply 14 to 45 =630 in ratio 6:30

What is the inverse function of y = 2x - 8

Answers

Answer:

Step-by-step explanation:

y = 2x-8

2x = y+8

x = 0.5y+4

inverse function: y = 0.5x+4

The equation and graph show the cost to rent movies from two different companies. The cost is a function of the number of movies rented.The description best compares the two functions?

Answers

The equation and graph show the cost to rent movies from two different companies. The cost is a function of the number of movies rented.The description best compares the two functions?

here the pic and pls brainly me hege

Let's play the Telephone Game together! https://garticphone.com/en/?c=013ab2298​

Answers

Answer:

Kk

Step-by-step explanation:

Depends on you bro

Have a nice day!?

Answer:

......free marks? .......

NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW. Use the following information for problems 19-21​

Answers

12 red + 16 blue + 18 white = 46 marbles

9. 3 marbles NO replacement: no white?
28/46 x 27/45 x 26/44
0.61 x 0.6 x 0.59 is about 22%

Each time we pick a red or blue we have one less to choose from next time

10. 4 marbles WITH replacement: all white?
18/46 x 18/46 x 18/46 x 18/46
0.39 x 0.39 x 0.39 x 0.39 is about 2%

11. 2 marbles NO replacement: red then blue

12/46 x 16/45
12 x 45 / 16 x 46
540/736
135/184 :)

8. Expand (2a – 3b + 4c)2
Helllpppp plz
Nowww it’s imp

Answers

Step-by-step explanation:

(2a–3b+4c)²=

4a²+9b²+16c²-12ab-24bc+8ac

If the first and last terms of a trinomial are perfect squares, the trinomial is a perfect square
trinomial.
True
O False

Answers

Answer:

A trinomial is a perfect trinomial if the first and last terms are positive, perfect squares and the middle term is twice the product of their square roots.

Therefore, if you mean perfect as in positive, the answer is True.

Are these events independent or dependent?

A) Take a marble out of a bag and putting it back in the bag then take another marble out of the bag.

B) draw a card from a deck of cards and setting it aside. Draw a card again from the same deck.

URGENT PLEASE HELP!!!

Answers

Answer:

a) Independent

b) Dependent

Step-by-step explanation:

a) is independent as the first marble does not affect the chance of getting the second marble as you are putting the marble you picked out back in the bag.

b) is dependent as it affects the chance of picking out other cards as you have removed one card from the list of possibilities.

Step-by-step explanation:

the shehejjene

brbnrb grutbdbd

please help with the steps thx

Answers

Answer:

amount financed: 47800

monthly payment: 454.97

FC: 6796.40

558390.76

198390.76

Step-by-step explanation:

1.)

the amount financed is the cost- amount paid today

61800-14000=47800

effective rate: .027/12=

assuming it's an annuity immediate...

x=payment

[tex]47800=x\frac{1-(1+.00225)^{-(10*12)}}{.00225}\\47800=105.0617517x\\x=454.97[/tex]

going to assume that the last part is asking for the interest

to find the interest do financed amount-total paid

454.97*10*12-47800=6796.4

2.)

Find the effective rate

.056/4=.014

assuming annuity immediate

[tex]6000\frac{(1+.014)^{15*4}-1}{.014}=558390.7595[/tex]

interest earned:

558390.7595-6000*60=198390.76

Find the area of the figure below. ANSWER in NUMBER ONLY

Answers

Answer:  80

==================================================

Work Shown:

area = base*height

area = 8*10

area = 80 square cm

The slanted sides aren't used. We only use the horizontal base 8 and vertical height 10. The base and height are always perpendicular to one another.

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