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3 years ago

11

which answer describes the graph of the function f(x)=-2*3^√x? just incase this isn't clear the three is above the square root s

ign. and its 2 times the rest of the equation. :)

1 answer:

andrey2020 [161]3 years ago

8 0

The function has a domain that goes from [0,∞]

And a range that goes from [-∞,0]

(See attached graph)

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Given two discrete random variables (X and Y) with

dezoksy [38]

Note that there are some duplicate events in the given distribution. I'm guessing you meant to describe the table below:

$\begin{array}{c|c|c|c|c}X\backslash Y&1&2&3&4\\1&0.1&0.05&0.02&0.02\\2&0.05&0.2&0.05&0.02\\3&0.02&0.05&0.2&0.04\\4&0.02&0.02&0.04&0.1\end{array}$

(imagine there are horizontal lines separating the rows in the table; for whatever reason, the command for making these lines doesn't work on this site)

The covariance is

$\mathrm{Cov}(X,Y)=E((X-E(X))(Y-E(Y)))=E(XY)-E(X)E(Y)=0.5096$

which follows from

$E(XY)=\displaystyle\sum_{x,y}xy\,P(X=x,Y=y)=6.66$

$E(X)=\displaystyle\sum_{x,y}x\,P(X=x,Y=y)=2.48$

$E(Y)=\displaystyle\sum_{x,y}y\,P(X=x,Y=y)=2.48$

The correlation is

$\mathrm{Corr}(X,Y)=\dfrac{\mathrm{Cov}(X,Y)}{\sqrt{E(X-E(X))^2E(Y-E(Y))^2}}\approx0.5150$

since

$E(X-E(X))^2=E(X^2)-E(X)^2=0.9896$

$E(Y-E(Y))^2=E(Y^2)-E(Y)^2=0.9896$

because

$E(X^2)=\displaystyle\sum_{x,y}x^2\,P(X=x,Y=y)=7.14$

$E(Y^2)=\displaystyle\sum_{x,y}y^2\,P(X=x,Y=y)=7.14$

Next, recall that

$P(Y=y\mid X=x)=\dfrac{P(X=x,Y=y)}{P(X=x)}$

where

$P(X=x)=\displaystyle\sum_yP(X=x,Y=y)$

Then we have, for instance,

$P(X=1)=\displaystyle\sum_yP(X=1,Y=y)=0.19$

so that

$P(Y=y\mid X=1)=\dfrac{P(X=1,Y=y)}{P(X=1)}=\begin{cases}0.5263&\text{for }y=1\\0.2632&\text{for }y=2\\0.1053&\text{for }y=3\\0.1053&\text{for }y=4\\0&\text{otherwise}\end{cases}$

and so

$E(Y\mid X=1)=\displaystyle\sum_yy\,P(Y=y\mid X=1)\approx1.7895$

You can similarly compute each conditional probability to find the the remaining conditional expectations.

$P(X=2)=0.32\implies E(Y\mid X=2)=2.125$

$P(X=3)=0.31\implies E(Y\mid X=3)\approx2.8387$

$P(X=4)=0.18\implies E(Y\mid X=4)\approx3.2222$

5 0

2 years ago

-3x+3y=12<br> 4x+2y=20<br><br> Please help its elimination. It's really hard I can't solve it

Karo-lina-s [1.5K]

-3x + 3y = 12<u /> ⇒ -12x + 4y = 48
4x + 2y = 20 ⇒   <u>12x + 6y = 60</u>
   <u>-2y</u> = <u>-12</u>
      -2 -2
      y = 6
      4x + 2(6) = 20
      4x + 12 = 20
   <u>     -12 -12</u>
   <u> 4x</u> =<u> 8</u>
      4    4
   x = 2
         (x, y) = (2, 6)

5 0

3 years ago

Solve each inequality, graph the solution, and write the solution in interval notation

Cloud [144]

Answer: $\frac{5}{4}\leq x\leq 2$

Step-by-step explanation:

Given :

5 ≤ 4x− 1 < 7

the equation could be spitted into 2

1. $5\leq 4x$

ii. $4x - 1$

solving them separately , we have

$5\leq 4x$

divide through by 4

$\frac{5}{4}\leq x$

solving (ii) we have

$4x - 1$

add 1 to both sides

$4x < 7 + 1$

$4x < 8$

$x$

combining the solutions , we have $\frac{5}{4}\leq x\leq 2$

7 0

3 years ago

A store has taps on display five of the Caps are red there are four more blue cap blue caps than cream caps there are three for

Nana76 [90]

Answer:

5 red

9 blue

7 yellow

3 green

6 0

3 years ago

Please determine x.

Rainbow [258]

Answer:

6

Step-by-step explanation:

8 0

2 years ago