What two numbers multiply to 108 and add to -39?

Consider a discrete random variable x with pmf px (1) = c 3 ; px (2) = c 6 ; px (5) = c 3 and 0 otherwise, where c is a positive

PtichkaEL [24]

Looks like the PMF is supposed to be

$\mathbb P(X=x)=\begin{cases}\dfrac c3&\text{for }x\in\{1,5\}\\\\\dfrac c6&\text{for }x=2\\\\0&\text{otherwise}\end{cases}$

which is kinda weird, but it's not entirely clear what you meant...

Anyway, assuming the PMF above, for this to be a valid PMF, we need the probabilities of all events to sum to 1:

$\displaystyle\sum_{x\in\{1,2,5\}}\mathbb P(X=x)=\dfrac c3+\dfrac c6+\dfrac c3=\dfrac{5c}6=1\implies c=\dfrac65$

Next,

$\mathbb P(X>2)=\mathbb P(X=5)=\dfrac c3=\dfrac25$

$\mathbb E(X)=\displaystyle\sum_{x\in\{1,2,5\}}x\,\mathbb P(X=x)=\dfrac c3+\dfrac{2c}6+\dfrac{5c}3=\dfrac{7c}3=\dfrac{14}5$

$\mathbb V(X)=\mathbb E\bigg((X-\mathbb E(X))^2\bigg)=\mathbb E(X^2)-\mathbb E(X)^2$
$\mathbb E(X^2)=\displaystyle\sum_{x\in\{1,2,5\}}x^2\,\mathbb P(X=x)=\dfrac c3+\dfrac{4c}6+\dfrac{25c}3=\dfrac{28c}3=\dfrac{56}5$
$\implies\mathbb V(X)=\dfrac{56}5-\left(\dfrac{14}5\right)^2=\dfrac{84}{25}$

If $Y=X^2+1$ , then $X^2=Y-1\implies X=\sqrt{Y-1}$ , where we take the positive root because we know $X$ can only take on positive values, namely 1, 2, and 5. Correspondingly, we know that $Y$ can take on the values $1^2+1=2$ , $2^2+1=5$ , and $5^2+1=26$ . At these values of $Y$ , we would have the same probability as we did for the respective value of $X$ . That is,

$\mathbb P(Y=y)=\begin{cases}\dfrac c3&\text{for }y=2\\\\\dfrac c6&\text{for }y=5\\\\\dfrac c3&\text{for }y=26\\\\0&\text{otherwise}\end{cases}$

Part (5) is incomplete, so I'll stop here.

8 0

3 years ago

Given WRST is a parallelogram and

daser333 [38]

It would be a parallelogram

3 0

3 years ago

What is the surface area of a rectangular prism? length : 3 width : 3 height = 5

elixir [45]

Since it is a rectangular prism, the front and back are the same. the sides are the same and the top and bottom are the same. You would find the area of the front and back first. Since they both have the same measurements, you can find the area of one of the faces and multiply by 2.
A=BH
A= 3x5
A=15
15x2=30
So the front and back's area is 30. Now you find the area of both sides. They are both rectangle so the formula is A=BH.
A=BH
A=3x5
A=15
15x2=30
Now you find the area of the top and bottom. It is also a rectangle so you will use the same formula.
A=BH
A=3x3
A=9
9x2=18
Finally, you add all these measurements together adn that is the surface area.
This surface area of this rectangle prism is 78.

4 0

3 years ago

Why is the grid in Example 1 a good way to represent a percent?

Tems11 [23]

Answer:

percent means per hundred

Between the 100 squares, 60 of them are shaded

so you do 60/100

it's kind of like correcting tests, you have 100 questions, you got 80 of them right so its going to be 80/100

when you calculate percentage, you do the fraction x 100

so it's 60/100 = 0.6 x100 = 60%

hope that answers your question

Don't hesitate to leave a comment if you are confused about something

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Plsss HELP ANYONE PLSSS !

Talja [164]

Answer:

can be fourth one cause it starts at 2 on y axis. ( fourth option)

Step-by-step explanation:

can't be the first one cause it starts at origin

can't be second one cause it starts at -2 on x axis

can't be third on cause it starts on 2 on x axis

can't be fifth cause it starts on -2 on y axis.

3 0

3 years ago