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grandymaker [24]

3 years ago

9

A company makes storage containers with sheet steel walls. The containers are shaped like rectangular prisms, as shown below. If

the company has a total of 944m2 of sheet steel available, how many storage containers can be made?

1 answer:

Anna35 [415]3 years ago

4 0

Answer:

(0.2)+(-8)=0.3+-3+0.3m

Step-by-step explanation:

a frend showed me

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

(a) Find <em>c</em> such that <em>f</em> 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 <em>X</em> by integrating the joint density with respect to <em>y</em> :

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

(c) Get the marginal density of <em>Y</em> by integrating with respect to <em>x</em> instead:

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

(d) The conditional distribution of <em>X</em> given <em>Y</em> can obtained by dividing the joint density by the marginal density of <em>Y</em> (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 <em>X</em> | <em>Y</em> in part (d) identical to the marginal density of <em>X</em> found in (b), so yes, <em>X</em> and <em>Y</em> are indeed independent.

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

8 0

3 years ago

Find the slope of the line (-7,3) (6,3)

statuscvo [17]

Answer:

0, it's a line parallel to the x-axis

Step-by-step explanation:

7 0

3 years ago

What is the slope, y-intercept and slope intercept equation to this graph. Plz help

fredd [130]

Answer:

y intercept is 3 and slope is 4/1

Step-by-step explanation:

3 0

3 years ago

Someone pls help me :)

klasskru [66]

1.

25%

.3 + .2 + .15 + .1 = .75

1.00 - .75 = .25

2.

120 students

There are 400 total students

.3 * 400 = 120

4.

tennis-

.1 * 400 = 40 students prefer tennis

football-

.25 * 400 = 100 students prefer football

140 students like football/tennis

5.

400 students

There are four quarters in a whole

.25% = 100

100 * 4 = 400

4 0

3 years ago

Which expression can be used to check the answer to 56 ÷ (-14) = n?

kozerog [31]

A. Multiplication is the ONLY function that reverses what division did. If you did 56/-14 = n, then n x -14 should equal 56.

6 0

2 years ago

Read 2 more answers