I need help desperately

I'm assuming

[tex]f(y)=\begin{cases}ky(1-y)&\text{for }0\le y\le1\\0&\text{otherwise}\end{cases}[/tex]

(a) f(x) is a valid probability density function if its integral over the support is 1:

[tex]\displaystyle\int_{-\infty}^\infty f(x)\,\mathrm dx=k\int_0^1 y(1-y)\,\mathrm dy=k\int_0^1(y-y^2)\,\mathrm dy=1[/tex]

Compute the integral:

[tex]\displaystyle\int_0^1(y-y^2)\,\mathrm dy=\left(\frac{y^2}2-\frac{y^3}3\right)\bigg|_0^1=\frac12-\frac13=\frac16[/tex]

So we have

k / 6 = 1   →   k = 6

(b) By definition of conditional probability,

P(Y ≤ 0.4 | Y ≤ 0.8) = P(Y ≤ 0.4 and Y ≤ 0.8) / P(Y ≤ 0.8)

P(Y ≤ 0.4 | Y ≤ 0.8) = P(Y ≤ 0.4) / P(Y ≤ 0.8)

It makes sense to derive the cumulative distribution function (CDF) for the rest of the problem, since F(y) = P(Y ≤ y).

We have

[tex]\displaystyle F(y)=\int_{-\infty}^y f(t)\,\mathrm dt=\int_0^y6t(1-t)\,\mathrm dt=\begin{cases}0&\text{for }y<0\\3y^2-2y^3&\text{for }0\le y<1\\1&\text{for }y\ge1\end{cases}[/tex]

Then

P(Y ≤ 0.4) = F (0.4) = 0.352

P(Y ≤ 0.8) = F (0.8) = 0.896

and so

P(Y ≤ 0.4 | Y ≤ 0.8) = 0.352 / 0.896 ≈ 0.393

(c) The 0.95 quantile is the value φ such that

P(Y ≤ φ) = 0.95

In terms of the integral definition of the CDF, we have solve for φ such that

[tex]\displaystyle\int_{-\infty}^\varphi f(y)\,\mathrm dy=0.95[/tex]

We have

[tex]\displaystyle\int_{-\infty}^\varphi f(y)\,\mathrm dy=\int_0^\varphi 6y(1-y)\,\mathrm dy=(3y^2-2y^3)\bigg|_0^\varphi = 0.95[/tex]

which reduces to the cubic

3φ² - 2φ³ = 0.95

Use a calculator to solve this and find that φ ≈ 0.865.

Using probability concepts, it is found that

a) The value is k = 6.

b) P(Y ≤ .4|Y ≤ .8) = 0.554.

c) The 95th percentile is x = 0.86465.

The density function is:

[tex]f(y) = ky(1 - y)[/tex]

Item a:

The condition that makes it a probability density function is:

[tex]\int_0^1 f(y) dy = 1[/tex]

Thus:

[tex]\int_0^1 f(y) dy = \int_0^1 ky - ky^2 dy[/tex]

[tex]\int_0^1 f(y) dy = k(\frac{y^2}{2} - \frac{y^3}{3})|_{y = 0}^{y = 1}[/tex]

[tex]\int_0^1 f(y) dy = k(\frac{1}{2} - \frac{1}{3})[/tex]

Then

[tex]k(\frac{1}{2} - \frac{1}{3}) = 1[/tex]

[tex]k(\frac{3-2}{6}) = 1[/tex]

[tex]k = 6[/tex]

The value is k = 6.

Item b:

This probability is:

[tex]\int_0.4^0.8 f(y) dy = 6(\frac{y^2}{2} - \frac{y^3}{3})|_{y = 0.4}^{y = 0.8}[/tex]

Then

[tex]p = 6\left(\frac{0.8^2}{2} - \frac{0.8^3}{3} - \frac{0.4^2}{2} + \frac{0.4^3}{3}\right)[/tex]

[tex]p = 0.554[/tex]

Thus, P(Y ≤ .4|Y ≤ .8) = 0.554.

Item c:

This is x for which:

[tex]\int_0^x f(y) dy = 0.95[/tex]

Thus:

[tex]6(\frac{x^2}{2} - \frac{x^3}{3}) = 0.95[/tex]

[tex]-2x^3 + 3x^2 - 0.95 = 0[/tex]

Solving a cubic equation with the help of a calculator, and considering [tex]0 \leq x \leq 1[/tex], this is x = 0.86465.

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Answer:

3 and i use flvs too, also that pfp is fire

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Answer:

the answer is 3

Answer:

7 pounds

Step-by-step explanation:

1 pound is $4 28/4 is 7

Answer:

41.5?

Step-by-step explanation:

is that it to the question or is there more?!?!

Answer:

0.42

Step-by-step explanation:

60-18= 42

42/100=0.42

(Hope this helped! :D)

Answer:

−2.8 or - 2 8/10

Step-by-step explanation:

hope that helps

Answer:

Use the number line and split the whole numbers into fractions

Step-by-step explanation:

Example: If a number line goes from -10 all the way to +10, and you are trying to find the distance between -2 1/4 and -7 3/4. You would split the number line into fourths and then locate -7 3/4. You would then count up to -2 1/4 to get 4 3/4.

Hopefully this makes sense!

Answer:

Example 1: - If the item's label displays the weight as 3 lb 2 oz, type the shop name and item's brand, enter 3 in the pounds field, leave the 00 (decimal) value unchanged, enter 2 in the ounces field, leave the 00 (decimal) value unchanged, fill out the Price field and Calculate to get the price per ounce

Answer:

12 ounces

Step-by-step explanation:

3.60 = .3x

divide by .3 on both sides

12 = x

Answer:

below in bold

Step-by-step explanation:

f(x) = 2x - 7 - 3

~Combine like terms

f(x) = 2x - 10

When x = 2...

f(x) = 2(2) - 10

f(x) = 4 - 10

f(x) = -6

When x = 3...

f(x) = 2(3) - 10

f(x) = 6 - 10

f(x) = -4

When x = 4...

f(x) = 2(4) - 10

f(x) = 8 - 10

f(x) = -2

Best of Luck!

Answer:

Step-by-step explanation:

Is b) corresponding angles are congruent.

The reason that justifies statement two: "Angle Y ≅ Angle 4", is option C "Alternate interior angles are congruent".

Angles that are of the same measurement are called congruent.

Suppose that two angles ∠A and ∠B are of the same measure, then

[tex]m\angle A = m\angle B[/tex] is the notation to say that they are of the same measurement, where the small m shows that it's the measurement's the angles they're preceding.

We can see that angle Y and angle 4 are two alternate angles within the two parallel lines cut across by the transversal, therefore, they are called alternate interior angles.

Since Alternate interior angles are always congruent to each other.

Thwithefore, the reason that justifies statement two: "Angle Y ≅ Angle 4", is "Alternate interior angles are congruent".

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Answer:(3,-4) you just have to follow the equation.

Slope = change in y over change in x.

Slope = (-6 - -9) / (-6 - -2)

Slope = (-6 + 9) / (-6 + 2)

Slope = 3/-4

Slope = -3/4

Answer:

C

Step-by-step explanation:

Answer:

Using mid point theorem, A line segment joining the mid points of the two sides of the triangle, is equal to half the length of the third side.

D and E are the mid points. Hence,

DE=

2

1

AC

DE=

2

1

(6.4)

DE=3.2cm

Answer:

AD=BE

Step-by-step explanation:

Because AB and BC are equal, their lengths are also equal and also it is an Isosceles triangle. Therefore the midpoint of AB or the half of AB which is either AD or DE are equal. Vice versa for BC. So AD=BE

Answer:

c = 6+2x

Step-by-step explanation:

c = total cost, 6 = entrance fee, 2x = 2 dollars per food/drink item

The number of marbles Peter had when he arrived home was 43 marbles

What is Percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

Given data ,

The number of marbles Peter had on his way home = 171

The amount of marbles he lost on his way home = ( 3/4 ) th

Now , the amount of marbles Peter have left = 1 - amount of marbles he lost on his way home

The amount of marbles Peter have left = 1 - 3/4

                                                                = ( 1 / 4) th

So , The number of marbles Peter had left when he arrived home is =

Amount of marbles Peter have left x Number of marbles Peter had

The number of marbles Peter had left when he arrived home is = (1/4) x 171

= 171 / 4

= 42.75

≈ 43 marbles

Hence , the number of marbles Peter had left when he reached home is 43

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Answer:

Multiplying and dividing fractions are essentially the same process which you multiply the numbers straight across and no need for common denominators. Except in division of fractions, the second fraction is flipped so that the denominator is on the top and the numerator is on the bottom (reciprocal).

Step-by-step explanation:

Example:

[tex]\frac{3}{4} * \frac{1}{5} = \frac{3}{20}[/tex]

[tex]\frac{3}{4}[/tex] ÷ [tex]\frac{1}{5} = \frac{3}{4} * \frac{5}{1} = \frac{15}{4}[/tex]

Answer: 3x - 8

Hope it helps!

Answer:

9 + 6 + 4 − 2 + 1 − 1 5

9x+{\color{#c92786}{6}}+4x-2x+{\color{#c92786}{1}}{\color{#c92786}{-15}}

9x+6+4x−2x+1−15

9 − 8 + 4 − 2

Step-by-step explanation:

Answer:

[tex]measure angle 1 = 62 ------> given\\measure angle 4 = 62 --------> vertical angle theorem[/tex]

Step-by-step explanation:

vertical angle theorem states that the angle vertical from another angle has to be congruent

p.s. i found it

Answer:

consistent and dependent

consistent and independent

inconsistent and independent

Step-by-step explanation:

Answer:

1

2

4

Step-by-step explanation:

has nice day

9514 1404 393

Answer:

  the correct answer is marked

Step-by-step explanation:

When the graph of the left side of the equation does not intersect the graph of the right side of the equation, there are no solutions.

__

Additional comment

Even if you extend the domain to complex numbers, there are no solutions. The f(x) = |x| function always returns a positive real value, even for complex numbers.

Answer:

7

Step-by-step explanation:

First do 3x2 to get 6, and then do 8-6, which is 2, and add that to 5 to get 7

Two Answers: Angle 1, Angle 4

Adjacent angles share a common segment, line, or ray. Think of two adjacent rooms sharing a common wall.

Answer:

its a

Step-by-step explanation:

The phrase is Scale by a factor of 1 /r and rotate clockwise by θ.

Complex numbers are numbers that consist of two parts — a real number and an imaginary number.

Given:

z=r(cos θ + i sin θ)

So, to divide a complex number the best phrase to describe is Scale by a factor of 1 /r and rotate clockwise by θ.

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