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2 years ago

0.7 (3s+4) − 1.1s = 7.9

2 answers:

7 0

Simplify to 2.1s + 2.8 - 1.1s = 7.9. Simplify again to s = 5.1. If this is right could you possibly give me brainliest? Hope this helped.

irina1246 [14]2 years ago

4 0

Answer:

5.1

it is 5.1 my quiz with this had it on their and it said it was right

Step-by-step explanation:

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2) X and Y are jointly continuous with joint pdf

Nady [450]

From what I gather from your latest comments, the PDF is given to be

$f_{X,Y}(x,y)=\begin{cases}cxy&\text{for }0\le x,y \le1\\0&\text{otherwise}\end{cases}$

and in particular, f(x, y) = cxy over the unit square [0, 1]², meaning for 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. (As opposed to the unbounded domain, x ≤ 0 *and* y ≤ 1.)

(a) Find c such that f is a proper density function. This would require

$\displaystyle\int_0^1\int_0^1 cxy\,\mathrm dx\,\mathrm dy=c\left(\int_0^1x\,\mathrm dx\right)\left(\int_0^1y\,\mathrm dy\right)=\frac c{2^2}=1\implies \boxed{c=4}$

(b) Get the marginal density of X by integrating the joint density with respect to y :

$f_X(x)=\displaystyle\int_0^1 4xy\,\mathrm dy=(2xy^2)\bigg|_{y=0}^{y=1}=\begin{cases}2x&\text{for }0\le x\le 1\\0&\text{otherwise}\end{cases}$

$f_Y(y)=\displaystyle\int_0^14xy\,\mathrm dx=\begin{cases}2y&\text{for }0\le y\le1\\0&\text{otherwise}\end{cases}$

(d) The conditional distribution of X given Y can obtained by dividing the joint density by the marginal density of Y (which follows directly from the definition of conditional probability):

$f_{X\mid Y}(x\mid y)=\dfrac{f_{X,Y}(x,y)}{f_Y(y)}=\begin{cases}2x&\text{for }0\le x\le 1\\0&\text{otherwise}\end{cases}$

(e) From the definition of expectation:

$E[X]=\displaystyle\int_0^1\int_0^1 x\,f_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy=4\left(\int_0^1x^2\,\mathrm dx\right)\left(\int_0^1y\,\mathrm dy\right)=\boxed{\frac23}$

$E[Y]=\displaystyle\int_0^1\int_0^1 y\,f_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy=4\left(\int_0^1x\,\mathrm dx\right)\left(\int_0^1y^2\,\mathrm dy\right)=\boxed{\frac23}$

$E[XY]=\displaystyle\int_0^1\int_0^1xy\,f_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy=4\left(\int_0^1x^2\,\mathrm dx\right)\left(\int_0^1y^2\,\mathrm dy\right)=\boxed{\frac49}$

(f) Note that the density of X | Y in part (d) identical to the marginal density of X found in (b), so yes, X and Y are indeed independent.

The result in (e) agrees with this conclusion, since E[XY] = E[X] E[Y] (but keep in mind that this is a property of independent random variables; equality alone does not imply independence.)

8 0

3 years ago

What is x if [-1 -2 4 8] + X =[-5 -1 2 1]

Scilla [17]

Answer:

X = [-5 -1 2 1] - [-1 -2 4 8] = [-4 1 -2 -7]

8 0

3 years ago

Round 34,576 to the nearest thousand

VARVARA [1.3K]

Answer:

35000

Step-by-step explanation:

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2 years ago

The table below shows the typical hours worked by employees at a company. A salaried employee makes $67,000 per year. Hourly emp

nadezda [96]

First, we must calculate the weekly pay of an employee that is paid a fixed amount. Given that there are 52 weeks in a year, the weekly pay for a regularly paid employee is: 67,000 / 52 = $1,288.46 Now, we calculate the number of hours an employee that is paid hourly works per week: 0 + 10 + 8 + 8 + 7 + 6.5 + 4.5 = 44 So this employee is paid: 25 x 40 + 37.5 x 4 = $1,150 Therefore, it is recommended that a new employee goes for the salaried pay since the weekly earnings are greater in this option. The answer is C.

7 0

3 years ago

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ser-zykov [4K]

Answer:

Step-by-step explanation:

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6 0

2 years ago