Which of the symbols correctly relates the two numbers below? Check all that apply. 100 ? 20

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

Write the expression in complete factored form.

ivolga24 [154]

Answer:

(x - 6) • (4x - y)

Step-by-step explanation:

brainly???

Step by step solution :

Step 1 :

Equation at the end of step 1 :

(4x • (x - 6)) - y • (x - 6)

Step 2 :

Equation at the end of step 2 :

4x • (x - 6) - y • (x - 6)

Step 3 :

Pulling out like terms :

3.1 Pull out x-6

After pulling out, we are left with :

(x-6) • ( 4x * 1 +( y * (-1) ))

Final result :

(x - 6) • (4x - y)

4 0

3 years ago

A system of two linear equations is graphed on a coordinate grid. The lines intersect at one point. Which statement about the sy

jasenka [17]

True I hope this helps

5 0

3 years ago

The College Board provided comparisons of Scholastic Aptitude Test (SAT) scores based on the highest level of education attained

poizon [28]

Answer:

a. $H_{0}:$ u1≤u2

$H_{a} :u1>u2$

b P<0.05 rejected H

Step-by-step explanation:

College High School

485 442

534 580

650 479

554 486

550 528

572 524

497 492

592 478

487 425

533 485

526 390

410 535

515

578

448

469

The mean is the average . the sum of number over the number of observation

x1=525

x2=487

s.d1=59.42

s.d2=51.74

n1=16

n2=12 $\alpha =0.05$

Determine the hypothesis

$H_{0}:$ u1≤u2

$H_{a} :u1>u2$

find the degree of freedom $(\frac{s1^2}{n1} +\frac{s2^2}{n2} )^2/(\frac{s1^2}{n1} )^2/n1-1+(s2^2/n2)^2/n2-1\\\\(\frac{59.42^2}{16} +\frac{51.7476^2}{12} )^2/(\frac{59.42^2}{16} )^2/16-1+(51.74^2/12)^2/12-1$

25

p-value is the probability of obtaining the value of the test statistics. In the column of t-value in the row df=25

0.025<P<0.05

if the P value is actually less than or the same as the significant level, then the null hypothesis is rejected

P<0.05 rejected H

8 0

3 years ago

A factory manager conducted a test on a random sample of 150 products. Of the products tested, 2 were found to be defective. Bas

lions [1.4K]

Answer:

40

Step-by-step explanation:

Write and solve a proportion:

2 / 150 = x / 3000

150x = 6000

x = 40

6 0

3 years ago

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