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2 years ago

A 6-inch candle is burning at a linear rate. The candle measures four inches two

Mathematics

1 answer:

Elis [28]2 years ago

8 0

2 in per hour.

it takes an hour to go down 2 in

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Suppose X, Y, and Z are random variables with the joint density function f(x, y, z) = Ce−(0.5x + 0.2y + 0.1z) if x ≥ 0, y ≥ 0, z

kompoz [17]

$f_{X,Y,Z}(x,y,z)=\begin{cases}Ce^{-(0.5x+0.2y+0.1z)}&\text{for }x\ge0,y\ge0,z\ge0\\0&\text{otherwise}\end{cases}$

is a proper joint density function if, over its support, $f$ is non-negative and the integral of $f$ is 1. The first condition is easily met as long as $C\ge0$ . To meet the second condition, we require

$\displaystyle\int_0^\infty\int_0^\infty\int_0^\infty f_{X,Y,Z}(x,y,z)\,\mathrm dx\,\mathrm dy\,\mathrm dz=100C=1\implies \boxed{C=0.01}$

b. Find the marginal joint density of $X$ and $Y$ by integrating the joint density with respect to $z$ :

$f_{X,Y}(x,y)=\displaystyle\int_0^\infty f_{X,Y,Z}(x,y,z)\,\mathrm dz=0.01e^{-(0.5x+0.2y)}\int_0^\infty e^{-0.1z}\,\mathrm dz$

$\implies f_{X,Y}(x,y)=\begin{cases}0.1e^{-(0.5x+0.2y)}&\text{for }x\ge0,y\ge0\\0&\text{otherwise}\end{cases}$

Then

$\displaystyle P(X\le1.375,Y\le1.5)=\int_0^{1.5}\int_0^{1.375}f_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy$

$\approx\boxed{0.12886}$

c. This probability can be found by simply integrating the joint density:

$\displaystyle P(X\le1.375,Y\le1.5,Z\le1)=\int_0^1\int_0^{1.5}\int_0^{1.375}f_{X,Y,Z}(x,y,z)\,\mathrm dx\,\mathrm dy\,\mathrm dz$

$\approx\boxed{0.012262}$

7 0

2 years ago

I need help I don’t know how to do this

vfiekz [6]

Answer:

Step-by-step explanation: The bigger triangle is 6 times bigger than the smaller one.

4 0

3 years ago

Which value is a perfect square? 12 24 49 63

marysya [2.9K]

Answer: 49 is a perfect square.

Step-by-step explanation: We say that 49 is a perfect square because it is the product of an integer multiplied by itself, 7×7. If we had a square with an area of 50, this wouldn't be a perfect square because no integer, multiplied by itself, will give a product of 50.

6 0

2 years ago

Read 2 more answers

How much Lemonade did Kayla sell? In the problem... Ethan sold 2/3 gallon of lemonade. Kayla sold some lemonade too. Together, t

VikaD [51]

1 and 3/12 all together
Convert ethans into 8/12
1 and 3/12- 8/12= 0.583...
0.583... is the amount Kayla sold
0.666... is amount Ethan sold
Ethan sold more
0.666...-0.583...= 0.083...
so Ethan sold 0.083 gallons more

6 0

2 years ago

Can u put this to least to greatest 7/12,0.75,5/6

Elis [28]

7/12, 0.75, 5/6 is the answer.

4 0

3 years ago

Read 2 more answers