Hello Pls help and thanks

Let Y be a random variable with a density function given by

Neporo4naja [7]

From the given density function we find the distribution function,

$F_Y(y)=P(Y\le y)=\displaystyle\int_{-\infty}^y f_Y(t)\,\mathrm dt=\begin{cases}0&\text{for }y$

(a)

$F_{U_1}(u_1)=P(U_1\le u_1)=P(3Y\le u_1)=P\left(Y\le\dfrac{u_1}3\right)=F_Y\left(\dfrac{u_1}3\right)$

$\implies F_{U_1}(u_1)=\begin{cases}0&\text{for }u_1$

$\implies f_{U_1}(u_1)=\begin{cases}\frac{{u_1}^2}{18}&\text{for }-3\le u_1\le3\\0&\text{otherwise}\end{cases}$

(b)

$F_{U_2}(u_2)=P(3-Y\le u_2)=P(Y\ge3-u_2)=1-P(Y$

$\implies F_{U_2}(u_2)=\begin{cases}0&\text{for }u_2$

$\implies f_{U_2}(u_2)=\begin{cases}\frac32(u_2-3)^2&\text{for }2\le u_2\le4\\0&\text{otherwise}\end{cases}$

(c)

$F_{U_3}(u_3)=P(Y^2\le u_3)=P(-\sqrt{u_3}\le Y\le\sqrt{u_3})=F_Y(\sqrt{u_3})-F_y(\sqrt{u_3})$

$\implies F_{U_3}(u_3)=\begin{cases}0&\text{for }u_3$

$\implies f_{U_3}(u_3}=\begin{cases}\frac32\sqrt u&\text{for }0\le u\le1\\0&\text{otherwise}\end{cases}$

5 0

3 years ago

The first two diamonds are filled in, can you figure out how the numbers are related when

balu736 [363]

Answer:

Step-by-step explanation:

Upper box in the diamond: Add the two numbers ⇒ (-2) + 3 = -1

Bottom box in the diamond : Multiply the two numbers ⇒ (-2) * 3 = -6

3) Upper box = (-6) + (-3) = (-9)

Bottom box = (-6) *(-3) = 18

4) Upper box = 1 +(-11) = -10

Bottom box = 1 *(-11) = -11

5) Upper box = 7+8 = 15

Bottom box = 7*8 = 56

7 0

2 years ago

Translate and solve: 336 is what percent of 96?

Vlad1618 [11]

The answer is 28.57 !!!

5 0

3 years ago

Write an equation of a line in point-slope, slope-intercept, and standard form that has

Inga [223]

Answer:

(a) $y + 4x - 14 = 0$

(b) $y = -4x + 14$

(c) $y + 4x = 14$

Step-by-step explanation:

The formula for calculating the equation of line in point - slope form is given as :

$y-y_{1} = m(x-x_{1} )$

where m is the slope

Given from the question :

m = - 4

$x_{1}$ = 2

$y_{1}$ = 6

Substituting into the formula , we have :

$y - 6 = - 4(x - 2)$

$y - 6 = -4x + 8$

$y + 4x - 6 - 8 = 0$

$y + 4x - 14 = 0$

Therefore :

(a) the equation of the line in point - slope form is $y + 4x - 14 = 0$

(b) to write it in slope - intercept form , we will make y the subject of the formula , which will give : $y = -4x + 14$

(c) the equation of line in standard form is ; $y + 4x = 14$

5 0

3 years ago

Explain and show plz

STALIN [3.7K]

C,D and F are correct.

C is what you would think of when reading it, you walked 12 and walked 1/4(12) more.

12 + 12(1/4) =

12 + 3 =

15

D is equal to C when simplified,

12(1+1/4) =

12 + 3 =

15

F is the same as the D, it just simplified the numbers in the parenthesis

12(1+1/4) =

12(4/4 + 1/4) =

12(5/4) =

15

8 0

3 years ago

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