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3 years ago

Suppose that in 8 minutes 72 gallons of water came out of a pipe.

Mathematics

1 answer:

ki77a [65]3 years ago

4 0

Answer:

Step-by-step explanation:

72/8=9

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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

Choose the number below that represents the digit in the hundreds place of

BaLLatris [955]

Answer:

b. 3

Step-by-step explanation:

7 0

3 years ago

Please help!

topjm [15]

Answer:

option A is correct .

<h2>knowing that</h2>

 ${6}^{2} + {8}^{2} = {10}^{2}$ 

<h2>draw the 6-foot side and the 8-foot side and a right angle between them the 10-foot side with complete the right triangle</h2>

3 0

2 years ago

= 3x +15 = 4x-10 What is the value of x?

Viefleur [7K]

Answer:

3x+15= 4x-10

3x-4x= -10-15

-x= -25(minus will be cut on both sides)

so x= 25

7 0

3 years ago

If there are 90 calories in Three-fourths cup of yogurt, how many calories are in 3 cups of yogurt? 30 calories 202 calories 270

Vitek1552 [10]

Answer:

360 calories

Step-by-step explanation:

you divide 3 by 3/4ths and you get 4. You then multiply 90 by 4 and the solution is 360 calories.

3 0

3 years ago

Read 2 more answers