Suppose you have a 6-face unfair dice with numbers 1,2,3,4,5,6 on each of its faces. If the probability distribution of throwing a number up is as follows: 1 with probability 1/12 2 with probability 1/12 3 with probability 1/12 4 with probability 1/12 5 with probability 1/12 6 with probability 7/12 What are the mathematical expectation and variance of the dice based on the above probability distribution

Answers

Answer 1

Answer:

Expectation is equal to 4.75

Variance is equal to 3.02

Step-by-step explanation:

Consider the attached image.

Let [tex]x_i[/tex] denotes each of the outcome.

Expectation [tex]=E(X)[/tex] = ∑[tex]x_if(x_i)[/tex]

[tex]=1(\frac{1}{12}) +2(\frac{1}{12}) +3(\frac{1}{12}) +4(\frac{1}{12}) +5(\frac{1}{12}) +6(\frac{7}{12})[/tex]

[tex]=\frac{1}{12}+\frac{2}{12}+\frac{3}{12}+\frac{4}{12}+\frac{5}{12}+\frac{42}{12}\\\\=\frac{57}{12}\\\\=4.75[/tex]

[tex]E(X^2)=[/tex] ∑ [tex]x_i^2f(x_i)[/tex]

[tex]=1^2(\frac{1}{12}) +2^2(\frac{1}{12}) +3^2(\frac{1}{12}) +4^2(\frac{1}{12}) +5^2(\frac{1}{12}) +6^2(\frac{7}{12})[/tex]

[tex]=(\frac{1}{12}) +4(\frac{1}{12}) +9(\frac{1}{12}) +16(\frac{1}{12}) +25(\frac{1}{12}) +36(\frac{7}{12})\\\\=\frac{307}{12}[/tex]

Variance  [tex]=E(X^2)-[E(X)]^2[/tex]

[tex]=(\frac{307}{12})-(\frac{57}{12})^2\\\\ =\frac{307}{12}-\frac{3249}{144}\\\\ =\frac{3684-3249}{144}\\\\ =\frac{435}{144}\\\\ =3.02[/tex]


Related Questions

Find the solution of the system of equations . - 5x + 9y = 11 x - 3y = - 7
how do i solve this

Answers

Answer:

Solution: x=5, y=4

Step-by-step explanation:

System of Equations

We need to solve:

- 5x + 9y = 11

x - 3y = - 7

There are several ways to solve a system of linear equations. We'll take advantage of the second equation since it has the x with coefficient 1 and solve it for x:

x = - 7 + 3y

Now replace it into the first equation:

- 5(- 7 + 3y) + 9y = 11

Operate:

35 - 15y + 9y = 11

Simplify:

35 - 6y = 11

Rearrange:

- 6y = 11 - 35 = -24

Solve:

y = -24 / -6

y = 4

Finally, since

x = - 7 + 3y

x = - 7 + 3*4

x = - 7 + 12

x = 5

Solution: x=5, y=4

PLZ HELP FAST
Suppose x and y give the populations of two different cities where x >y and y > 0. Compare the expressions and select which of the given pair is greater. X/ x +y (select) x+y /X​

Answers

Answer:

(x + y)/x is greater than x/(x + y)

Step-by-step explanation:

Given.

x > y

y > 0

Required

Which is greater?

x/(x + y) or (x + y)/x

Since x is greater than y & y > 0

Then definitely,

x + y > x

By the above analysis:

(x + y)/x is an improper fraction because the numerator (x + y) is greater than the denominator (x)

While

x/(x + y) is a proper fraction because the numerator (x) is lesser than the denominator.

All improper fractions are greater than all proper fractions,

Hence:

(x + y)/x is greater than x/(x + y)

To further explain this:

Take

x = 3 and y = 2

x/(x + y) = 3/(3 + 2) = 3/5 = 0.6

(x + y)/x = (3 + 2)/3 = 5/3 = 1.67

See that (x + y)/x is greater than x/(x + y)

And this is so for all values of x and y

Where x > y and y > 0

Answer:

is less than

Step-by-step explanation:

g Suppose you are rasterizing a triangle with vertices (1, 1), (5, 1), and (2, 9), and the intensity values (e.g., redness) of those vertices are 5, 9, and 14, respectively. Using the linear interpolation scheme, what is the intensity value of an interior point at (3, 5)? Show all your work.

Answers

Answer:

6.333

Step-by-step explanation:

Our triangle vertices are

(1,1)(5,1)(2,9)

We are to perform interpolation at point(3,5)

x and y values are interpolated

On vertices (5,1)(2,9)

x = 3

x1 = 5

X2 = 2

Y1 = 1

Y2 = 9

Formula for interpolation

Y = [y1+(x-x1)(y2-y1)]/x2-x

Y = 1+(3-5)(9-1)/2-5

Y = 1+[-2*8/-3]

Y = 1+16/3

From here we use use LCM to get:

19/3 = 6.333

what Mitochondria of a
of a cell

Answers

Answer:

membrane-bound cell organelles

Will give brainliest if your answer is correct, please help me with this question it is past due (I have more questions like this that are also pat due, check my profile and go to questions to see them once I post the questions)

Answers

Answer:

Equal angles; Vertical angles ( which means equal ) ; Angles do not share special relationship; and right angles.... Hope this helps!

Step-by-step explanation:

PLS HELP!! What is the value of X

Answers

21 don’t even trip lil b just go with the flow

Selina didn't use the distributive property correctly. Where did she go wrong? Explain your thinking.​

Answers

Answer:

PEMDAS

Step-by-step explanation:

Well, I don't know if there should be a picture of the problem that should go with the question. But a trick for solving distributive property is to use the trick PEMDAS In order.

For Example:

P-Paraenthese

E-Exponent

M-Multiply

D-Divide

A-Add

S-Subtract

NOTE!

Remember to always Multiply and divide BEFORE adding and subtracting.

Hoped this helped!

Suppose you have 3 quizzes and want an average of 7 points. List at least five ways this average can be accomplished. keep in mind that each score can be no more than 10 points.

Answers

Answer:

4,9,8 = 4+9+8 = 21

9,9,3 = 9+9+3 = 21

6,7,8 = 6+7+8 = 21

8,8,5 = 8+8+5 = 21

5,7,9 = 5+7+9 = 21

Step-by-step explanation:

The question says you get 7 points per quiz out of 3 quizzes.

7+7+7 = 21

Now that we know that we need a total score of 21, we therefore need to distribute it among the three quizzes.

Remember;

None of these scores are to be higher than 10. We need to add up scores below 10.

4,9,8 = 4+9+8 = 21

9,9,3 = 9+9+3 = 21

6,7,8 = 6+7+8 = 21

8,8,5 = 8+8+5 = 21

5,7,9 = 5+7+9 = 21

All of these gives 7 as average.

ah
nsjakensnsjskdkdkdjjsjsjshshsjzjs

Answers

Answer:

Step-by-step explanation:

Rectangle A measures 8 inches by 4 inches. Rectangle B is a scaled copy
of Rectangle A and is multiplied by the scale factor 7. What are the
dimensions of Rectangle B?

Answers

Rectangle B = 56inches by 28inches
It’s pretty easy you just multiply 8 by 7 and 4 by 7.

c. One sixth of a number is 15. What is the number?
Please explain step by step.

Answers

Answer:

90

if 15 is 1 6th then yo need 5 more 15s to find out the whole number

A famous recipe for New Orleans jambalaya calls for 1 1/4 cups of Gulf shrimp. The recipe serves 5 people. Trinetta and Agnes want to serve 12 people, so they increase all the ingredients proportionally. How much Gulf shrimp is required for the new recipe?

A. 1 2/5
B. 5/12
C. 3 cups
D. 4/5 cups
E. 7 cups​

Answers

Answer: C. 3 cups

Step-by-step explanation:

Given: In recipe for 5 people, Required Gulf shrimp = [tex]1\dfrac14[/tex] cups

Since, [tex]1\dfrac14=\dfrac{5}{4}[/tex]

Required Gulf shrimp = [tex]\dfrac54[/tex] cups

Then, for 1 people Gulf shrimp required = [tex]\dfrac{5}{4}\div 5[/tex]

[tex]=\dfrac54\times\dfrac{1}{5}[/tex]

[tex]=\dfrac14[/tex] cup

For 12 people, it is required = [tex]12\times\dfrac14 = 3\text{ cups}[/tex]

Hence, 3 cups of gulf shrimp is required for new recipe.

So, correct option is C. 3 cups

Researchers recorded the speed of ants on trails in their natural environments. The ants studied, Leptogenys processionalis, all have the same body size in their adult phase, which made it easy to measure speeds in units of body lengths per second (bl/s). The researchers found that, when traffic is light and not congested, ant speeds vary roughly Normally, with mean 6.20 bl/s6.20 bl/s and standard deviation 1.58 bl/s.1.58 bl/s. (a) What is the probability that an ant's speed in

Answers

This question is Incomplete

Complete Question

Researchers recorded the speed of ants on trails in their natural environments. The ants studied, Leptogenys processionalis, all have the same body size in their adult phase, which made it easy to measure speeds in units of body lengths per second (bl/s). The researchers found that, when traffic is light and not congested, ant speeds vary roughly Normally, with mean 6.20 bl/s and standard deviation 1.58 bl/s. (a) What is the probability that an ant's speed in light traffic is faster than 5 bl/s? You may find Table B useful. (Enter your answer rounded to four decimal places.)

Answer:

0.7762

Step-by-step explanation:

We solve using z score formula

z = (x-μ)/σ, where

x is the raw score

μ is the population mean

σ is the population standard deviation.

Population mean = 6.20 bl/s

Standard deviation = 1.58 bl/s.

x = 5 bl/s

z = 5 - 6.20/1.58

z = -0.75949

The probability that an ant's speed in light traffic is faster than 5 bl/s is P( x > 5)

Probability value from Z-Table:

P(x<5) = 0.22378

P(x>5) = 1 - P(x<5)

= 1 - 22378

= 0.77622

Approximately to 4 decimal places = 0.7762

The probability that an ant's speed in light traffic is faster than 5 bl/s is 0.7762

divide and answer in simplest form: 1/3 divided by 5

Answers

Answer:

1/15

Step-by-step explanation:

1. You can divide 1/3 by 5 by changing the division symbol to its reciprocal, multiplication, and also divide by the reciprocal of the number after the symbol, 5. The reciprocal of 5 is 1/5.

2. Now you can do 1/3 multiplied by 1/5. Multiply the numerators by the denominators. The numerators are 1 and 1, so you multiply 1 by 1 which equals 1. Now you multiply the denominators, 3 and 5, which is equal to 15. If the numerator is now 1, and the denominator is 15, the new fraction is 1/15, getting you to your answer

2.685
x 102
Expanded form

Answers

Answer:

2.685 + 2.685 + 2.685 + 2.685 + 2.685 + 2.685. . . . . 102 times.

Step-by-step explanation:

Think of this as 102 times of 2.685.

So you would add 2.685 together 102 times.

(I didn't want to type out 2.685 that many times)

Hope I helped :)

Please consider Brainliest :)

the nth term of a sequence is 20-n^2
a) find the third term of the sequence
b) which term in the sequence is the first to have a negative value ​

Answers

Answer:

a) 20 - 3^2 = 11

b) 5th, 20 - 5^2 = -5

Step-by-step explanation:

The answer assumes your terms begin at 1. If the terms begin at zero

a) 16

b) 6th term

if you chose to be extremely technical you would take the square root of 20.1 or 20.00000009 but I'm assuming they want whole numbers

Answer:

a)11

b)5th term

Step-by-step explanation:


A government may create and regulate natural monopolies because:

Answers

Answer:

they can handle the costs of providing essential services

Step-by-step explanation:

A government may create and regulate natural monopolies because the government has the right to manage and regulate the resources available to the country in order to provide welfare and proper services to own citizens.

Given that,
A government may create and regulate natural monopolies because:,
The incomplete statement is to be complete.

What is right?

An authority or claim controlled by the all-around people as the result of a constitution, law, ordinance, judicial precedent, or another type of law.

Here,
A government in any country has one motto rule of the country is to the people, for the people, and of the people. Whatever government does suppose to be for the welfare and proper livelihood in the country for its citizens. So in this manner,

Thus, a government may create and regulate natural monopolies because the government has the right to manage and regulate the resources available to the country in order to provide welfare and proper services to its own citizens.

Learn more about rights here,
https://brainly.com/question/8903161
#SPJ5

What is the measure of the missing angle?
36°
57°

Answers

Answer:

7767788877787887+-77-7

The first one is right I did it

The Acme Battery Company has developed a new cell phone battery. On average, the battery lasts 60 minutes on a single charge. The standard deviation is 4 minutes. Suppose the manufacturing department runs a quality control test. They randomly select 7 batteries. The standard deviation of the selected batteries is 6 minutes. a. What would be the chi-square statistic represented by this test? b. What are the degrees of freedom for the chi-square statistic? c. Suppose they repeated the test with a new random sample of 7 batteries. What is the probability that the standard deviation in the new test would be greater than 6 minutes? (Use the applet)

Answers

Answer:

X² = 13.5

Degree of freedom = 6

0.04

Step-by-step explanation:

Give the following :

Number of samples (n) = 7

Population standard deviation (σ) =.4 minutes

Sample standard deviation (s) = 6

Mean battery life = 60 minutes

A) Chisquare (X²) :

X² = ((n - 1) * s²) / σ²

X² = ((7 - 1) * 6²) / 4²

X² = (6 * 6²) / 4²

X² = (6 * 36) / 16

X² = 216 / 16

X² = 13.5

B.) The degree of freedom:

degree of freedom = n - 1

Degree of freedom = 7 - 1 = 6

C.) using a chisquare distribution calculator :

With degree of freedom (df) = 6

X² = 13.5

Hence,

P(X² > 13.5) = 0.04 ( from calculator)

What are the coordinates of the point (-3, 4) after a translation 5 units
right and 6 units down?

Answers

Answer:

(2,-2)

Step-by-step explanation:

what is the measure of CED

Answers

Step-by-step explanation:

The measure of CED is p degree.

In triangle ABC and EDC,(Given)(Vertical opposite angles)

By AA rule of similarity,

Corresponding angles of similar triangles are same.

Therefore the measure of CED is p degree.

pls give brainest

Which is equal to 0.63?

Answers

Answer:

63%

Step-by-step explanation:

A percentage is x/100.  So 0.63 = x/100.  So multiply by 100, and you'll get 63%.

0.63 is equal to 63%. When finding the percentage of a decimal multiply by 100. Therefore, 0.63 x 100 equals 63%•

0.63 x 100 = 63%

How do I Evaluate f(5).

Answers

plug in 5 for x in your equation and solve

Which of the following does NOT represent a whole number?
9, 6.0, 12/4, -12/3 help plz

Answers

Answer:

-12/3

Step-by-step explanation:

Whole numbers can't be negative!

Answer:

d. your welcome

Step-by-step explanation:

Hulu has two different subscription prices. You can pay $6.88 per month for the year or $60.00 per year. How much less per month is the annual subscription?

Answers

Answer:

$22.56

Step-by-step explanation:

$6.88 ⋅ 12 = $82.56

So you would have to pay $82.56 per year if you paid $6.88 per month.

$82.56 - $60.00 = $22.56

You would save $22.56 if you paid $60.00 per year.

Hope I helped :)

Please consider Brainliest :)

HURRY ON A TIMER PLEASE HELP

which shows all the like terms in the expression ​

Answers

Answer:

the second one -3and1 :4x and 7x

Step-by-step explanation:

Answer:

-3 and -1; 4x and 7x

Step-by-step explanation:

like terms are the numbers with the same variable

eg. 4x^2 and 6x aren't like terms, but 2x^4 and 3x^4 are

Find the measure of the missing angle

Answers

1 = 108 degrees 2 = 72 degrees

Explanation: 108 degrees and 1 are identical angles so they are the same and for 2 you take 180-108 = 72

Jeff places a pineapple with mass of 890g on a balance scale. He balances the scale by placing 2 oranges, an apple and lemon on other side. Each orange weighs 280g. The lemon weighs 195g less than each orange. What is the mass of the apple?

Answers

Answer:

bnbvmnbnjnmbkjbvkjhbjn

Step-by-step explanation:

lnjkkllknnhljknk

Anyone ??? Help with this one

Answers

Answer:

(4x-3y)(4x+3y)

Step-by-step explanation:

This is a difference of squares equation. As it says, ([tex]x^{2} -y^2[/tex]) is equal to (x-y)(x+y)

Simply apply the formula to your numbers, [tex]16x^{2} -9y^2[/tex].

It gives the hint of [tex]16x^{2}[/tex] is equal to (4x)^2. and, 9y^2 is equal to (3y)^2, since if you square 4x and 9y, they get 16x^2 and 9y^2 respectively.

Now, you need to do (4x-3y)(4x+3y)

Hope this helps

Pleas help I am brainliesting and show the steps

Answers

Answer:

2 and 1/3 ---->>> 2 1/3

Step-by-step explanation:

At 4, its 4 cm

Within 3 hours it has gained 7 cm

7/3=2.33333

2 1/3 would be the mixed number

can i get brainliest please?

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