Suppose X has a continuous uniform distribution over the interval [−2,2]
a) Determine the mean, variance, and standard deviation of X
b) Determine the value of a such that P(−a

Answers

Answer 1

Answer:

Mean = 0

Variance = 4/3

Standard Deviation √4/3

a= 0.9

Step-by-step explanation:

If X has a uniform distribution over [a,b] then its Mean is a+b/2 and variance is (b-a)²/12

Here a=  -2 and b= 2

Now finding the mean = a+b/2=-2+2/2= 0

Variance = (b-a)²/12=( 2-(-2))²/12= 4²/12= 16/12= 4/3

Standard Deviation = √Variance= √4/3

b) [tex]\int\limits^a_b f({x}) \, dx[/tex]=  \int\limits^a_a {\frac{1}{a- (-a)} } \, dx

                =1/2a[x]^a_-a= 2a/2a= 1  (applying the limits to the function)

P(−a<X<a) =[tex]\int\limits^a_b {x} \, dx[/tex]=1/2 * 2a= a    (applying the limits to the function)

P(−a<X<a)= 0.9

a= 0.9

In the given question the limits are -a to a . When we apply these in the above instead of [a,b] we get the above answer.

Answer 2

Using the uniform distribution, we have that:

The mean is 0.The variance is of 1.25.The standard deviation is of 1.12.

An uniform distribution has two bounds, a and b.

In this problem, interval [−2,2], hence [tex]a = -2, b = 2[/tex].

The mean is:

[tex]E(X) = \frac{a + b}{2}[/tex]

Hence:

[tex]E(X) = \frac{-2 + 2}{2} = 0[/tex]

The variance is:

[tex]V(X) = \frac{(b - a)^2}{12}[/tex]

Hence

[tex]V(X) = \frac{(2 - (-2))^2}{12} = \frac{16}{12} = 1.25[/tex]

The standard deviation is the square root of the variance, hence [tex]\sqrt{1.25} = 1.12[/tex]

A similar problem is given at https://brainly.com/question/14767944


Related Questions

Which line is perpendicular to y=7x-3 if the perpendicular line passes through the point (7, 7)? a) y=-7x-1 b) y=-7x+8 c) y=-1/7x+8 d) y=-1/7x+1

Answers

Perpendicular lines have an opposite reciprocal slope, therefore, the slope of the perpendicular line is:

-1/7

So far, y = -1/7x + b. Now we need to plug in (7, 7) into x and y for our equation.

7 = -1/7(7) + b

Simplify the right side

7 = -1 + b

Add 1 to both sides

8 = b

The equation of the perpendicular line is:

y = -1/7x + 8

PLEASE HELP!! Need help with my homework!

Answers

Answer:

Line segment: AD (without arrow)

Ray: BA (with one sided arrow)

Rays with common endpoint: AC and AD (with one sided arrow)

Intersection: AE (double sided arrow)

Collinear points: B, A, C

PLEASE MARK AS BRAINLIEST

what is the expression equivalent to 5(6+4)​

Answers

Answer:

2(15+10)

Step-by-step explanation:

when you multiply the integers by 5 you get 30 + 20 so you just divide them by 10.

Answer
50
How to get it
So start to add in the parenthesis 6+4 is 10
Then erase the parentheses since we got the answer but turn it into an multiplication sign
5 times 10 is 50
Hope this helped :)

What is the quotient?
5^-6
5^3

Answers

Step-by-step explanation:

1/5^(3+6)= 1/5^9

the solution

Step-by-step explanation:

1/5^(3+6)=1/5^9

the solution

If B is between A and C, and AB = x and BC = 12, and AC = 25, then find the value of AB.
AB = ?

Answers


AB=12 because it is half of it

HELP!!! Need help with my home work!

Answers

Answer:

xy - y^2/x

Step by step explanation:

Lupe has 500 Mexican pesos. If 1 U.S. dollar equals 12.87333 pesos, about how many dollars can Lupe buy for her pesos?

Answers

Answer:

the answer is C. $38.84

Step-by-step explanation:

Brian saw 106 birds and half as many squirrels. Which of the following is a good estimation of how many more birds he saw than squirrels?

Answers

Answer:

53

Step-by-step explanation:

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Answers

Area of triangle = 1/2 × b × h

b = base and h = height

Area = 1/2 × (x+4) × (2)

Area = x + 4

Area of rectangle = lb

l = Length and b = Breadth

Area = 10 (x + 2)

Area = 10x + 20

Given:

The area of rectangle is 8 times greater than the area of the triangle.

Solution:

According to the question,

10x + 20 = 8(x+4)

or, 10x + 20 = 8x + 32

or, 10x - 8x = 32 - 20

or, 2x = 12

or, x = 12/2 = 6

Answer:

The value of x is 6.

Hence, Option D. 6 is correct.

Answer:

x = 6

Step-by-step explanation:

Area of rectangle = length * width

                             = 10 *(x +2)

                             = 10*x + 10*2

                             = 10x + 20   unit²

Area of triangle = [tex]\frac{1}{2}bh[/tex]

                          [tex]=\frac{1}{2}*2*(x +4)\\\\=1*(x+4)\\\\= x +4[/tex]

Area of rectangle  = 8*area of triangle

10x + 20 = 8* (x+ 4)

10x + 20 = 8x + 32           {Subrtact 20 from both sides}

        10x = 8x + 32 - 20

        10x = 8x + 12   {subtract 8x form both sides}

  10x - 8x = 12

         2x = 12     {divide both sides by 2}

      2x/2 = 12/2

          x = 6

Ivan sold 51 boxes of oranges on Friday and 29 boxes on Saturday during a citrus sale. There were 10 oranges in each box. How many oranges did he sell in all??

Answers

Answer:

800 oranges

Step-by-step explanation:

51 x 10 = 510

29 x 10 = 290

510 + 290 = 800

Factorise Fully x^2 + x

Answers

Answer:

X(x+1)

Step-by-step explanation:

If it is wrong I'm sorry.

Sita Rahim drove due north for 3 hours at 46 miles per hour. From the
same spot, Yasmina Young drove due south for 2 hours at 43 miles per
hour. How far apart were they after their trip?

Answers

Answer:

224 miles

Step-by-step explanation:

What you would do is take the 3 hours times the 46 mph to get 138 miles.

3*46=138

Next, multiply the 2 hours by the 43 mph to get 86 miles.

2*43=86

Lastly, you're going to add the two.

138+86=224 miles.

10. Use Structure What could be a first step to
solving the equation 3x + -0.5(x + 3) + 4 = 14?
Explain.

Answers

First distribute -0.5 to x and 3 giving you the new equation 3x + -0.5x-1.5

Simplify the expression. (5x^3+4x^2+6x-3)+(-2x^3+3x^2-7x+9)-(5x+3)(4x^2+x-1)

Answers

Answer:

-17x³-10x²+x+9

Step-by-step explanation:

(5x³+4x²+6x-3)+(-2x³+3x²-7x+9)-(5x+3)(4x²+x-1)

(5x³+4x²+6x-3)+(-2x³+3x²-7x+9)-(20x³+5x²-5x+12x²+3x-3)

(3x³+7x²-x+6)-(20x³+17x²-2x-3)

-17x³-10x²+x+9

Quick I need help, it states what polygon is shown by the street sign

Answers

I’m pretty sure it’s just asking what shape each sign is.

One way is a rectangle
I can’t tell if the do not enter is a circle or square... maybe you can see it better
Stop is an octagon
etc...

You have 2.5 pounds of egg whites
You need 37 ounces to make one serving of consommé
How many servings can you make?

Answers

You can only make 1 serving, because 2.5 pounds equals 40 ounces and you need 37 ounces to make 1 serving.

How is this number read out loud 0.034

Answers

Answer:

0.034

Step-by-step explanation:

thirty-four thousandths

or

zero point zero three four

h(x)= -x^2+3x for h(-3)

Answers

i believe the answer is -18.

An environmental study of a certain community suggests that t years from now, the average level of carbon monoxide in the air will be Q(t)=0.05t^2 + 0.1t + 3.4 parts per million. By approximately how much will the carbon monoxide lvel change during the coming 6 months?

Answers

Answer:

3.4625

Step-by-step explanation:

Given the equation:

Q(t)=0.05t^2 + 0.1t + 3.4 parts per million

Where t = time in years

By approximately how much will the carbon monoxide lvel change during the coming 6 months?

t = 6 months = 6/12 = 0.5 year

Q(0.5) = 0.05(0.5)^2 + 0.1(0.5) + 3.4 parts per million

Q(0.5) = 0.05(0.25) + 0.05 + 3.4

Q(0.5) = 0.0125 + 0.05 + 3.4

Q = 3.4625

Carbon monoxide level will change by approximately 3.4625 parts per million in 6 months

PLEASE HELP
Twice a number n is at least 30

Answers

Answer: n = 15

Step-by-step explanation: 2x15 = 30

Answer:

15

Step-by-step explanation:

15 times 2 is 30. Therefore, 15 can be the correct answer!

Please mark me brainliest if I helped you! Thank you so much!

:)

Find the distance between the points (-3,-6) and (-3,-2)

Answers

Answer:

The answer is

4 units

Step-by-step explanation:

The distance between two points can be found by using the formula

[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\ [/tex]

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(-3,-6) and (-3,-2)

The distance is

[tex]d = \sqrt{( { - 3 + 3})^{2} + ({ - 6 + 2})^{2} } \\ = \sqrt{ {0}^{2} + ({ - 4})^{2} } \\ = \sqrt{16} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

We have the final answer as

4 units

Hope this helps you

Answer: the answer is 4 units

Explanation: it is 4 units because since they are both on the x axis and 6 - 2 is equal to 4. It’s four units.

6. How many 1/2 hour periods will make up 4 hours?

Answers

Answer:

8 1/2 hour periods will make up 4 hours.

Step-by-step explanation:

half an hour is 30 minutes, and there are 60 minutes in an hour. 4 hours=240 minutes. 240÷30=8.

hope this helps! best of luck <3

Solve for x.
-2 (x + 1/4)+1=5
Enter your answer as a fraction in simplest form in the box.
X = ​

Answers

Answer:

[tex]x=-\frac{9}{4} \\ or \:\\x = -2\frac{1}{4}[/tex]

Step-by-step explanation:

[tex]-2 (x + 1/4)+1=5\\\\-2\left(x+\frac{1}{4}\right)+1=5\\\\\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}\\\\-2\left(x+\frac{1}{4}\right)+1-1=5-1\\\\Simplify\\-2\left(x+\frac{1}{4}\right)=4\\\\\mathrm{Divide\:both\:sides\:by\:}-2\\\frac{-2\left(x+\frac{1}{4}\right)}{-2}=\frac{4}{-2}\\\\Simplify\\x+\frac{1}{4}=-2\\\\\mathrm{Subtract\:}\frac{1}{4}\mathrm{\:from\:both\:sides}\\\\x+\frac{1}{4}-\frac{1}{4}=-2-\frac{1}{4}\\\\Simplify\\x=-\frac{9}{4}\\\\x = -2\frac{1}{4}[/tex]

11-3(a-2)=27 I NEED TO SHOW WORK HELP

Answers

Answer:

3.3 recurring

Step-by-step explanation:

1) expand bracket

11-3a+6=27

2)rearrange equation

11+6=27+3a

11+6-27=3a

17-27=3a

-10=3a

-10/3=a

a=3.3 recurring

Answer:

a= - [tex]\frac{10}{3}[/tex] or -3.33

Step-by-step explanation:

[tex]11-3(a-2)=27[/tex]

subtract 11 on both sides; 27-11=16

[tex]-3(a-2)=16[/tex]

divide both sides by -3

[tex](a-2)=-\frac{16}{3}[/tex]

add 2 on both sides

[tex]a=-\frac{16}{3} +2[/tex]

a=[tex]-\frac{10}{3}[/tex]

f(x) = 3x + 10
g(x) = x - 2
Find f(g(0))

Answers

Answer:

4

Step-by-step explanation:

f(g(x)) = 3(x-2) + 10

f(g(0)) = 3x - 6 + 10

f(g(0)) = 3(0) - 6 + 10

f(g(0)) = 0 - 6 + 10

f(g(0)) = 4

What is 3/8-2 what does it equal

Answers

Answer:

the answer would be -1 5/8 in fraction form and -1.625 in decimal form

Answer:

-13/8

Step-by-step explanation:

2 = 16/8

3/8-16/8 = -13/8

9(x +3) = 4x -3 cant figure it out

Answers

Answer:

[tex]x=-6[/tex]

Step-by-step explanation:

[tex]9\left(x+3\right)=4x-3[/tex]

Expand:

[tex]9x+9\times3=4x-3[/tex]

[tex]9x+27=4x-3[/tex]

Subtract 27 from both sides:

[tex]9x+27-27=4x-3-27[/tex]

[tex]9x=4x-30[/tex]

Subtract 4x from both sides:

[tex]9x-4x=4x-30-4x[/tex]

[tex]5x=-30[/tex]

Divide both sides by 5:

[tex]\frac{5x}{5}=\frac{-30}{5}[/tex]

[tex]x=-6[/tex]

what is 3/5 as a percent

Answers

Answer:60%

Step-by-step explanation:

3 divided by 5 ten times by 100 and you get 60%

What is the solution of 3x + y = 9 and 3x - 5y = 15?
OA 1 = 10 y = -1
B.
r = g y = 1
10
C. I = -1. y = 5
OD. x = 1, y = 2
COICO

Answers

Step-by-step explanation:

3x + y = 9

3x − 5y = 15

Solve with elimination.  Subtract the second equation from the first.

6y = -6

y = -1

Plug into either equation to find x.

3x + -1 = 9

3x = 10

x = 10/3

Solve the inequality. 6x + 14 > 20
???????

Answers

Answer:

x > 1

Step-by-step explanation:

6x + 14 > 20

      -14    -14

6x > 6

/6    /6

x>1

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