find the value of k for which the given function is a probability density function. f(x) = 2k on [−1, 1]

Answers

Answer 1

Answer:

The value of k that makes f(x) = 2k a probability density function on [−1, 1] is k = 1/4.

Step-by-step explanation:

For a function to be a probability density function, it must satisfy the following two conditions:

The integral of the function over its support must be equal to 1:

∫ f(x) dx = 1

The function must be non-negative on its support:

f(x) ≥ 0, for all x in the support of f(x)

Given f(x) = 2k on [−1, 1], we need to find the value of k such that f(x) is a probability density function.

Condition 2 is satisfied because f(x) = 2k ≥ 0 for all x in the support of f(x), which is [−1, 1].

To satisfy condition 1, we need:

∫ f(x) dx = ∫_{-1}^{1} 2k dx = 2k [x]_{-1}^{1} = 2k(1 - (-1)) = 4k = 1

Solving for k, we have:

4k = 1

k = 1/4

Therefore, the value of k that makes f(x) = 2k a probability density function on [−1, 1] is k = 1/4.

To Know more about probability refer here

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Related Questions

math is so hard man but can someone help me

Answers

Answer:

a

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

No, because

the first function if you further calculate you have

y= 3(x +5) is y = 3x+15 ; since you have to distribute

the second function if you have to translate is y=3x+5 because if you read it out loud the equation now you will say y equals 3 times x plus 5 like was given

What is the measure of Angles are not necessarily drawn to scale.

Answers

x is 58° (your welcome:)

Answer: 58

Step-by-step explanation:

180-114= 66

66+56=122

180-122= 58

Factor: k^2 + 7x + 10
A:(k+10)(k+4)
B:(k+2)(k+5)
C:(k+2)(k-5)
D:(k-2)(k-5)

Answers

Answer:

the answer is B. (k+2)(k+5)

Answer:

a

Step-by-step explanation:

IMPORTANT!! in a unit circle, what is the relationship between arc length and central angle?

Answers

The measure of an arc refers to the arc length divided by the radius of the circle. The arc measure equals the corresponding central angle measure, in radians. That's why radians are natural: a central angle of one radian will span an arc exactly one radius long.

Suppose ABC and DEF are complementary angles. If ABC = (5x + 7)º
and ABC = (3x + 3)', What are the measures of the two angles?

Answers

Answer:

The first will be 16.6

The second will be 29

Step-by-step explanation:

Hope this Helped

[tex]5x + 7 = 90[/tex]

[tex]3x + 3 = 90[/tex]

Jessica is bringing cupcakes to school for her birthday. She is placing them in a rectangular box that can fit 4 more cupcakes long that it can wide. They will not all fit in the box, so she is also bringing a bag that can hold 12 cupcakes. The amount of cupcakes she is bringing can be represented as x(x + 4) + 12. Solve for the number of cupcakes wide and long the box will hold. Part A) What does x represent?​

Answers

Answer:

the amount of cupcakes

Step-by-step explanation:

you said the amount of cupcakes can be represented by

hola me ayudan pliss como saco el resultado de 584 × (?) =179288 y (?) ÷ 143 = 572​

Answers

1) = 307
2) = 81796

1) 179288/584 = 307
2) 572 x 143 = 81796

Answer:

1)307

2)81796

Step-by-step explanation:

584 × (?) =179288

[tex]\frac{179288}{584}[/tex] =307

(?) ÷ 143 = 572​

572x143 =81796

¡Espero que esto sea de ayuda! :)

PLS HELP!!
Which expressions simplify to a rational answer?

Select each correct answer.

Answers

The second one only

Because they are both perfect squares.
Non perfect squares multiply by another non perfect square gives you a irrational number.

A grocery store is offering a sale on bread and soup. Kacey buys four cans of soup and three loaves of bread for $12.35. Fernando buys eight cans of soup and one loaf of bread for $13.05.
a. Write equations for both Kacey’s and Fernando’s purchases.

Answers

Answer:

Kacey

4x+3y=12.35

Fernando

8x+1y=13.05

Philippe will read One-half of the number of pages that Rafael reads. How many pages will Rafael read?

Answers

Answer: I cannot answer it because it needs more details. For ex say how much day he/she needs and how much pages he/she will read.

Step-by-step explanation: Unknown

Find the slope .
What does this mean?
Find the y intercept.
What does this mean?

Answers

slope = y2-y1 / x2-x1
intercept= y=mx+b
m(the slope) b( y-intercept)

The hypotenuse of a right angle triangle is 4 metres. If its other sides are equal find the length of each side.​

Answers

Answer:

[tex] \sqrt{8} [/tex]

or

[tex]2 \sqrt{2} [/tex]

Step-by-step explanation:

Since the legs are equal this is a 45-45-90 triangle.

The ratio of side length for a 45 45 90 triangle

[tex](1)(1)( \sqrt{2} )[/tex]

where 1 is the legs length and sqr root of 2 is the length of the hypotenuse.

Since we are trying to find the length of the legs side we can set up a proportion.

We know the hypotenuse is 4 so our proportion looks like

[tex] \frac{1}{x} = \frac{1}{x} = \frac{ \sqrt{2} }{4} [/tex]

Let see how far sqr root of 2 goes into 4.

[tex] \sqrt{2} \times x = 4[/tex]

[tex] \sqrt{2} \times x = \sqrt{16} [/tex]

[tex]x = \sqrt{8} [/tex]

so that means the answer for the legs length is

[tex] \sqrt{8} [/tex]

or

[tex]2 \sqrt{2} [/tex]

Answer:

Step-by-step explanation:

hello :

use  phtagor - rule:  let  x  the length of each side

x² +x² =4²

2x² =16

x² = 8  

x = √8

but :  8 = 4×2 = 2²×2

x = √(2²×2) = √2²× √2 =2√2      ......   √2² =2

x  =  2√2 metres.

Graph the function y = 4x4 – 8x2 + 4. Which lists all of the turning points of the graph?

(0, 4)
(–1, 0) and (1, 0)
(–1, 0), (0, 4), and (1, 0)
(–4, 0), (–1, 0), (0, 4), and (1, 0)

in case you are wondering, there is no graph.

Answers

Answer:

[tex]4(x + 1)^{2}(x - 1)^{2}[/tex]

Step-by-step explanation:

STEP 1:

The equation at the end of step 1

[tex]((4 (x^4)) - 2^3x^2) + 4[/tex]

STEP 2:

The equation at the end of step 2:

[tex](2^2x^4 - 2^3x^2) + 4[/tex]

STEP 3:

STEP 4: Pulling out like terms

4.1 Pull out like factors:

[tex]4x^4 - 8x^2 + 4 = 4(x^4 - 2x^2 + 1)[/tex]

Trying to factor by splitting the middle term

4.2 Factoring [tex]x^4 - 2x^2 + 1[/tex]

The first term is, [tex]x^4[/tex] its coefficient is 1.

The middle term is,  [tex]-2x^2[/tex]  its coefficient is -2.

The last term, "the constant", is +1.

Step-1: Multiply the coefficient of the first term by the constant   1 • 1 = 1

Step-2: Find two factors of  1  whose sum equals the coefficient of the middle term, which is -2.

-1 + -1 = -2 That's it

Step-3: Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -1  and  -1

                    x4 - 1x2 - 1x2 - 1

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x2 • (x2-1)

             Add up the last 2 terms, pulling out common factors :

                    1 • (x2-1)

Step-5 : Add up the four terms of step 4 :

                   (x2-1)  •  (x2-1)

            Which is the desired factorization

Trying to factor as a Difference of Squares:

4.3      Factoring:  x2-1

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 1 is the square of 1

Check :  x2  is the square of  x1

Factorization is :       (x + 1)  •  (x - 1)

Trying to factor as a Difference of Squares:

4.4      Factoring:  x2 - 1

Check : 1 is the square of 1

Check :  x2  is the square of  x1

Factorization is :       (x + 1)  •  (x - 1)

Multiplying Exponential Expressions:

4.5    Multiply  (x + 1)  by  (x + 1)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is  (x+1)  and the exponents are :

         1 , as  (x+1)  is the same number as  (x+1)1

and   1 , as  (x+1)  is the same number as  (x+1)1

The product is therefore,  (x+1)(1+1) = (x+1)2

Multiplying Exponential Expressions:

4.6    Multiply  (x-1)  by  (x-1)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is  (x-1)  and the exponents are :

         1 , as  (x-1)  is the same number as  (x-1)1

and   1 , as  (x-1)  is the same number as  (x-1)1

The product is therefore,  (x-1)(1+1) = (x-1)2

Final result :

 4 • (x + 1)2 • (x - 1)2

BRO PLS HELP ME I NEED TO TURN IT IN AN HOUR

Answers

Answer:

A

Step-by-step explanation:

Multiply all the points by 2.

Describe the steps necessary to solve the following system equations:

-3x - 4y = 2 and 3x + 3y = -3

Answers

Answer:

(- 2, 1 )

Step-by-step explanation:

Given the 2 equations

- 3x - 4y = 2 → (1)

3x + 3y = - 3 → (2)

Adding the 2 equations term by term will eliminate the x- term, that is

0 - y = - 1

- y = - 1 ( multiply both sides by - 1 )

y = 1

Substitute y = 1 into either of the 2 equations and solve for x

Substituting into (2)

3x + 3(1) = - 3

3x + 3 = - 3 ( subtract 3 from both sides )

3x = - 6 ( divide both sides by 3 )

x = - 2

solution is (- 2, 1 )

Answer:

x = -2 and y = 1

Step-by-step explanation:

3x + 3y = -3, x + y = -1,  x = -y -1

-3(-y-1) - 4y = 2, 3y + 3 - 4y - 2 = 0

-y +1 = 0, y = 1

x + y = -1, x + 1 = -1, x = -2

Kirk is getting a raise of 5% due to inflation. His normal salary is $56,000 per year. Which of the following calculations gives Kirk's new salary, in dollars? A. 56,000 +5 B. 56,000 + 56,000(0.05) C. 56,000 + 56,000(0.50) D. 56,000 + 56,000(5) E. 56,000(.05)

Answers

Answer:

The answer is B. 56,000 + 56,000(0.05) because 5% or expressed in decimals 0.05 multiplied by the quantity 56,000 gives us 5% of Kirk's normal salary and added to his normal salary will give us his new salary.

(His new salary is 58,800 and 5% of his normal salary is 2,800)

What are 3 of the 6 essential principles in Jefferson's Inaugural Address?

GIVE ME 3 OF THEM PLEASEEE

Answers

Answer:

He said that the nation had "room enough for our descendants to the thousandth and thousandth generation" and that his administration would pursue "honest friendship with all nations, entangling alliances with none." He affirmed that America's future depended upon "the preservation of the General government

Step-by-step explanation:

Who tryna help me with my work? 10th Grade work btw.....

Answers

Answer:

Thanks for the points- but im a duma$s

Step-by-step explanation:

A rectangle is covered by 24 unit squares. There are no gaps or overlap.

How can the area of the rectangle be found?


The area of the rectangle is equal to the number of unit squares that cover the rectangle. The area of the rectangle is 24 square units.

The area of the rectangle is half the number of unit squares that cover the rectangle. The area of the rectangle is 12 square units.

The area of the rectangle is double the number of unit squares that cover the rectangle. The area of the rectangle is 48 square units.

Answers

Answer: Choice A

The area of the rectangle is equal to the number of unit squares that cover the rectangle. The area of the rectangle is 24 square units.

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

Explanation:

Imagine drawing equally spaced grid lines to subdivide the rectangle. This splits the rectangle into smaller squares. In this case, each little square is 1 square unit. Having 24 of these squares leads to a total area of 24 square units.

We could have 8 rows and 3 columns of these squares to get 8*3 = 24 total. Or we could have 6 rows and 4 columns to get 6*4 = 24. Another configuration is 12 rows and 2 columns which leads to 12*2 = 24.

4d = 30 the answer would be c=7.5 right if not plz correct me if im wrong

Answers

Answer:

Correct!

Step-by-step explanation:

You did it the correct mathematical way, where you divide 4 by 30. Some people get confused and multiply 30 and 4, so good job!

Answer:

Step-by-step explanation: 4÷30=7.5 D = 7.5

Della has $575.38 in her checking account. What is the balance after she makes a deposit of $50.00 and a withdrawal of $85.45?
A)
$539.93
B)
$558.45
C)
$561.63
D)
$603.73

Answers

Answer:

A) 539.93

Step-by-step explanation:

575.38 + 50 - 85.45 = 539.93

Answer: A

$539.93

Step-by-step explanation:

Balance is $575.38 so add (+) $50 for her deposit and subtract (-) $85.45 to get the answer

Is (-1,3) a solution for y < 2x + 5?

Answers

No it’s not a solution

Amanda bought 4 pairs of jeans for $71.40. How much would she need to pay for 8 pairs of jeans?

Answers

Answer:  $142.80

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

Explanation:

To get this answer, we double the 71.40 to get 142.80

You can think of it like an equation and we multiply both sides by 2

4 jeans = 71.40 dollars

2*(4 jeans) = 2*(71.40 dollars)

8 jeans = 142.80 dollars

------------

Or you could solve it like this

(4 jeans)/(71.40 dollars) = (8 jeans)/(x dollars)

4/71.40 = 8/x

4x = 71.40*8

4x = 571.2

x = 571.2/4

x = 142.80

------------

Yet another way to solve is to first find the unit rate

4 jeans cost 71.40, so that must mean 1 pair of jeans cost 71.40/4 = 17.85 dollars. This is the unit rate since "unit" means "one". It's the price per pair of jeans.

Multiply that by 8 to find out how much 8 pairs will cost, and we get 17.85*8 = 142.80

Find the distance between the points A and B given below.

Answers

Answer:

use formula

Step-by-step explanation:

distance between the points A and B=

√((x2-x1)²+(y2-y1)²)

A light house worker is tracking a boat that is 5 km south of her. She is also tracking a boat
that is 6 km from the tower located 70° east of north. To the nearest kilometer, how
far apart are the two boats?

A. 7 km
B. 9 km
C. 8 km
D. 16 kM

Answers

Answer:

cccccccccccccccccccccccccccccc c

Pls help me ASAP pls

Answers

d= -11 I don’t remember if you have to flip the inequality symbol or not but the answer is -11

Find the length of the third side. If necessary, write in simplest radical form

Answers

Answer:

4^2 + 6^2 = x^2

Step-by-step explanation:

Pythagorean theorem is used. Solve for x.

1f (-2, y) lies on the graph of y = 3, then y =​

Answers

Answer:

y = 3

Step-by-step explanation:

the y-value of any ordered pair that lies on the line 'y = 3' will be equal to 3.

have to state if the triangles are similar or not.

2. You have to provide the postulate used if similar.

3. You have to complete the similarity statement. 4. You have to support your answers with work.

Answers

Answer:

Step-by-step explanation:

10). 1). Both the triangles are not similar.

     2). For the similarity of two triangles, corresponding sides of the triangles should be proportional and the included angles should be equal in measure.

         Although the angle given is equal but the corresponding sides of the triangles are not proportional, triangles are not similar.

          [tex]\frac{UW}{HF}= \frac{UV}{GF}[/tex] (For similar triangles)

          [tex]\frac{9}{21}= \frac{18}{42}[/tex]

          [tex]\frac{3}{7}=\frac{6}{7}[/tex]

          But [tex]\frac{3}{7}\neq \frac{6}{7}[/tex] therefore, both the triangles are not similar.

11). In ΔTUV and ΔCDE,

    If the given triangles are similar, their corresponding sides will be proportional and the included angle will be equal in measure.

    ∠C ≅ ∠T [Given]

    [tex]\frac{TU}{CD}= \frac{UV}{DE}[/tex]

    [tex]\frac{30}{10}=\frac{27}{9}[/tex]

    3 = 3

    True.

    Therefore, ΔTUV ~ ΔCDE (By SAS postulate of similarity]

can someone help me​

Answers

Step-by-step explanation:

40 ÷ 4 ( 4 sides) = 10

So each side measures 10inches

Answer:

10

Step-by-step explanation:

beacue 10x4

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