4x+1=9+4y solve for y

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]

a.

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

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

3 years ago

The endpoints of jk are j(–25, 10) and k(5, –20). what is the y-coordinate of point l, which divides jk into a 7:3 ratio

Trava [24]

The correct answer for this question is this one: (-4, -11)
In order to solve this,

Let k1 = 7/10 = fraction of the first part
Let k2 = 3/10 = fraction of the second part

Then, use solve for x and y

x = (k1(x2) +k2(x1)) / (k1+k2)
y = (k1(y2) +k2(y1)) / (k1+k2)

x = (7/10 * 5 + 3/10 * -25) / (7/10 + 3/10 )
x = -8 / 2
x = -4

y = (7/10 * -25 + 3/10 * 10) / (7/10 + 3/10)
y = -14 + 3
y = -11

Hope this helps answer your question. Have a nice day!

4 0

4 years ago

Read 2 more answers

Which option shows the graph of 4y + 8 < -3x

nasty-shy [4]

Answer: On apex it would be answer A the dotted graph with the shaded portion to the bottom left.

Step-by-step explanation:

4 0

3 years ago

Find x (2x+1) (5x+5)

mezya [45]

explanation;

Solution for 2x+1=5x-5 equation

Simplifying

2x + 1 = 5x + -5

Reorder the terms:

1 + 2x = 5x + -5

Reorder the terms:

1 + 2x = -5 + 5x

Solving

1 + 2x = -5 + 5x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-5x' to each side of the equation.

1 + 2x + -5x = -5 + 5x + -5x

Combine like terms: 2x + -5x = -3x

1 + -3x = -5 + 5x + -5x

Combine like terms: 5x + -5x = 0

1 + -3x = -5 + 0

1 + -3x = -5

Add '-1' to each side of the equation.

1 + -1 + -3x = -5 + -1

Combine like terms: 1 + -1 = 0

0 + -3x = -5 + -1

-3x = -5 + -1

Combine like terms: -5 + -1 = -6

-3x = -6

Divide each side by '-3'.

x = 2

Simplifying

x = 2

8 0

4 years ago

Read 2 more answers

7. Two classes have car washes to raise money for class trips. A portion of the

postnew [5]

Based on the information given, the percentage for the trip earnings rate for class A and B is 80% and 70% respectively.

<h3>How to calculate percentage.</h3>

From the information given, the trip earnings rate for A will be calculated thus:

= 16/20 × 100.

= 80%

The trip earnings rate for B will be calculated thus:

= 14/20 × 100

= 70%

Learn more about percentages on:

brainly.com/question/24304697

8 0

2 years ago