Eight less than one-half a number is two.

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

5x + 3y = -2<br> 3x + 2y = -1

Effectus [21]

Answer:

(-1,1)

Step-by-step explanation:

5x+2y= -2, x= -1/3 - 2/3y

5( -1/3 - 2/3y) +3y= -2

y= 1

x= -1/3 - 2/3 × 1

x= -1

7 0

3 years ago

Read 2 more answers

What is the value of x? <br><br>Enter your answer in the box.

scoray [572]

Answer:

x=11

Step-by-step explanation:

Since the lines in the middle are parallel, we know that both sides are proportional to each other.

6:48 can be simplified to 1:8

Since we know the left side ratio is 1:8, we need to match the right side with the same ratio

We can multiply the ratio by 5 to match 5:3x+7

5:40

5:3x+7

Now we can set up the equation: 40=3x+7

Subtract 7 from both sides

3x=33

x=11

5 0

3 years ago

sveticcg [70]

Answer:

Option C. $m$

Step-by-step explanation:

we know that

If two figures are similar, then the ratios of its corresponding sides is equal and its corresponding angles are congruent

so

m<A=m<J

m<B=m<K

m<C=m<L

therefore

The measure of angle J is the same that the measure of angle A

$m$

5 0

4 years ago

Read 2 more answers

A cyclist rides 225 m each minute.About how long does it take to ride 15km? Show all fo your work

Elan Coil [88]

Speed = 225 metres per minute

Distance = 15 km = 15,000 metres

---------------------------------------------------

s=d/t

ts=d

Therefore: t=d/s

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Time = Distance / Speed

Time = (15,000 metres) / (225 metres per minute)

--------------------------------------------------

Let's work it out:

$Time=\frac { 15,000\quad metres }{ \frac { 225\quad metres }{ 1\quad minute\left( s \right) } } \\ \\ =\frac { 15,000\quad metres }{ 1 } \cdot \frac { 1\quad minute\left( s \right) }{ 225\quad metres } \\ \\ =\frac { 15,000 }{ 225 } minutes$

$\\ \\ =\frac { 200 }{ 3 } minutes\\ \\ \frac { 200 }{ 3 } minutes\quad =\quad 66\quad minutes,\quad 40\quad seconds$

6 0

4 years ago