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2 years ago

Can someone pls help me -n-

Mathematics

2 answers:

olchik [2.2K]2 years ago

6 0

Answer:

(2, -7)

Step-by-step explanation:

thanks for your time sorry if i got it wrong.

Have a great day.

(>.<) <3 Kris

olga55 [171]2 years ago

4 0

I like math-way it will help you a lot

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Suppose that Y has density function

zvonat [6]

I'm assuming

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

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

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

Compute the integral:

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

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

$\displaystyle F(y)=\int_{-\infty}^y f(t)\,\mathrm dt=\int_0^y6t(1-t)\,\mathrm dt=\begin{cases}0&\text{for }y$

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

$\displaystyle\int_{-\infty}^\varphi f(y)\,\mathrm dy=0.95$

We have

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

which reduces to the cubic

3φ² - 2φ³ = 0.95

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

8 0

3 years ago

For the function y = -2x + 20, what is the output when the input is 50.

Artemon [7]

Y=-2x+20
Input 50
Y=-2(50)+20
Y=-100+20
y=-80

I hope this helps :) feel free to ask if you need anything cleared up

3 0

2 years ago

Chris sells books for a commission of $2.60 per book and $50 a month. His salary is determined by the function M=2.60 b+50, wher

vazorg [7]

$115 hope this helps

3 0

3 years ago

Find the volume make it an improper fraction then a mixed number please do a step by step explanation and I will give you brainl

Andrews [41]

Answer:

8463/32=264 15/32

Step-by-step explanation:

Let's make every fraction improper first.

7 3/4=31/4

5 2/8=42/8

6 1/2=13/2

Simplify 42/8

42/8=21/4

21/4

31/4

13/2=26/4

21/14*31/4*26/4=(21*31*26)/64=16926/64=8463/32

3 0

2 years ago

Divide € 165 into the ratio 1:2:12

fenix001 [56]

Answer:

11 : 22 : 132

Step-by-step explanation:

1 + 2 + 12 = 15

165 ÷ 15 = 11

1 × 11 = 11

2 × 11 = 22

12 × 11 = 132

11 : 22 : 132

3 0

2 years ago