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3 years ago

Joe's auto shop, it takes him

Mathematics

1 answer:

Greeley [361]3 years ago

7 0

12x + 24y < = 240

** because 2 hrs and 120 minutes = 240 minutes

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Suppose X and Y are random variables with joint density function. f(x, y) = 0.1e−(0.5x + 0.2y) if x ≥ 0, y ≥ 0 0 otherwise (a) I

Hatshy [7]

a. $f_{X,Y}$ is a joint density function if its integral over the given support is 1:

$\displaystyle\int_{-\infty}^\infty\int_{-\infty}^\infty f_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy=\frac1{10}\int_0^\infty\int_0^\infty e^{-x/2-y/5}\,\mathrm dx\,\mathrm dy$

$=\displaystyle\frac1{10}\left(\int_0^\infty e^{-x/2}\,\mathrm dx\right)\left(\int_0^\infty e^{-y/5}\,\mathrm dy\right)=\frac1{10}\cdot2\cdot5=1$

so the answer is yes.

b. We should first find the density of the marginal distribution, $f_Y(y)$ :

$f_Y(y)=\displaystyle\int_{-\infty}^\infty f_{X,Y}(x,y)\,\mathrm dx=\frac1{10}\int_0^\infty e^{-x/2-y/5}\,\mathrm dy$

$f_Y(y)=\begin{cases}\dfrac15e^{-y/5}&\text{for }y\ge0\\\\0&\text{otherwise}\end{cases}$

Then

$P(Y\ge8)=\displaystyle\int_8^\infty f_Y(y)\,\mathrm dy=e^{-8/5}$

or about 0.2019.

For the other probability, we can use the joint PDF directly:

$P(X\le5,Y\le8)=\displaystyle\int_0^5\int_0^8f_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy=1+e^{-41/10}-e^{-5/2}-e^{-8/5}$

which is about 0.7326.

c. We already know the PDF for $Y$ , so we just integrate:

$E[Y]=\displaystyle\int_{-\infty}^\infty y\,f_Y(y)\,\mathrm dy=\frac15\int_0^\infty ye^{-y/5}\,\mathrm dy=\boxed5$

5 0

3 years ago

Which is a perfect square? 6’1 6’2 6’3 6’5

34kurt

Answer:

6^2 is the answer

Step-by-step explanation:

just trust me ik

4 0

3 years ago

A coordinate plane with a line drawn passing through the points (0, 3) and (3, 2).

Margaret [11]

Answer:

None of the equations given is the equation of the function. The correct equation is: $y=-\frac{x}{3}+3\\$

Step-by-step explanation:

First we must find the slope of the line that passes through these points.

The slope between two points $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is given by:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

where $m$ is the slope

In this case since we have the points: $(0, 3)$ and $(3, 2).$

$x_{1}=0\\y_{1}=3\\x_{2}=3\\y_{2}=2$

and the slope will be:

$m=\frac{2-3}{3-0}=\frac{-1}{3}$

and now we have the slope we use the slope-point equation:

$y=m(x-x_{1})+y_{1}$

$y=-\frac{1}{3}(x-0)+3\\ y=-\frac{x}{3}+3\\$

7 0

4 years ago

Read 2 more answers

Find the surface area of this triangular prism

Yuki888 [10]

Answer:

300 in2

Step-by-step explanation:

area of 2 identical triangle + area of 3 rectangle = surface area

(5*12/2)*2 + 8*12 + 5*8 + 8*13 = 300 in2

4 0

4 years ago

Jethro wants a swimming pool in his backyard, so he digs a rectangular hole with dimensions 40 feet long, 20 feet wide, and 5 fe

Genrish500 [490]

4000 so the answer is C
Hope this helps

6 0

4 years ago