Mathematics I need help

What is the slope of the line that passes through the pair of points? (1, 7), (10, 1)

Vladimir [108]

Slope=(y2-y1)/(x2-x1)
(x,y)
x1=1
y1=7
x2=10
y2=1

slope=(1-7)/(10-1)=-6/9=-2/3
answer is A

6 0

3 years ago

Read 2 more answers

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

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

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

(c) Get the marginal density of Y by integrating with respect to x 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 X given Y can obtained by dividing the joint density by the marginal density of Y (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 X | Y in part (d) identical to the marginal density of X found in (b), so yes, X and Y are indeed independent.

The result in (e) agrees with this conclusion, since E[XY] = E[X] E[Y] (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 range, variance, and standard deviation for the given sample data. Include appropriate units in the results.Listed bel

timama [110]

Answer:

D.No, because some models of cell phones will have a larger market share than others. Measures from different models should be weighted according to their size in the population.

Step-by-step explanation:

(a) Range is the difference between the smallest and largest observation.

Here Smallest observation = 0.63

and Largest observation = 1.48

⇒ Range = 0.85

(b) Standard Deviation is calculate by,

$Standard deviation(\sigma) = \sqrt{\frac{1}{n}\sum_{i=1}^{n}{(x_{i}-\bar{x})^{2}} }$

where, $\bar{x}$ is mean of the observation.

Here, Mean = 0.988

⇒ Standard Deviation = 0.313

(c) Variance is the square of Standard deviation.

Thus, Variance = (Standard Deviation)² = 0.098

(d) Here last option(D) is true i.e. No, because some models of cell phones will have a larger market share than others. Measures from different models should be weighted according to their size in the population.

8 0

3 years ago

Andrew rents bowling shoes for $4. He bowls 2 games. Andrew spent a total of $22. How much was the cost of each game, b? Complet

Aneli [31]

Answer:

2b + 4 = 22

b= 9, the cost of each game is $9

Step-by-step explanation:

8 0

3 years ago

1) Find the missing side.

kari74 [83]

Answer:

25inch

Step-by-step explanation:

Ok so there is something called a Pythagorean theorem.

It's a²+b²=c²

It works on right triangles

C is the longest side or the side not touching the right angle

and a and b is the other 2 sides

so the missing side is 24²+7²=Missing side or c²

24²=576 and 7²= 49

576+49=625

$\sqrt{625}$ =25

3 0

3 years ago