1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
charle [14.2K]
3 years ago
12

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

Mathematics
1 answer:
Neporo4naja [7]3 years ago
5 0

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}

You might be interested in
A bag of marbles contains 4 red marbles, 5 yellow marbles, 2 green marbles, and 7 blue marbles. You draw one marble from the bag
klio [65]
This is an example of probability.
4 0
3 years ago
Can someone help, "Solve for x and y when 3y=12 and x+y = 6"
Lapatulllka [165]

Answer:

x=2

y=4

3 times 4 equals 12 and 2 plus 4 would equal six

7 0
3 years ago
If the radius of the circle is multiplied by a factor of 3, then the area of the circle is multiplied by a factor of
Oksi-84 [34.3K]
\bf \textit{area of a circle}\\\\
A=\pi r^2\quad 
\begin{cases}
r=radius\\
-----\\
r=\stackrel{r\times 3}{3r}
\end{cases}\implies A=\pi (3r)^2
\\\\\\
A=\pi (3^2r^2)\implies A=9(\pi r^2)

notice, if the original area was πr², then the new area has a factor in front of it, that much.
8 0
3 years ago
What is the absolute value of 7.4
NNADVOKAT [17]
The answer is -7.4 because you switch from positive to negative
7 0
2 years ago
Read 2 more answers
The image of the point (1, -3) under a translation is (-4,-2). Find the
Kay [80]

Answer: -8,6

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
Other questions:
  • Simplify the sum. (8u3 + 8u2 + 6) + (4u3 – 6u + 3)
    15·2 answers
  • 1 point
    12·1 answer
  • What is .689 in word form
    10·1 answer
  • Can two obtuse angles be verticle?
    10·1 answer
  • Evaluate the. Expression x+ 9, if x= 8. 1, 2, 17, 89
    9·2 answers
  • Explain how to find the range of a data set. what is an advantage of using the range
    6·2 answers
  • Seven and two-thousandths is written as​
    12·2 answers
  • Please help with 1 and 2 :)
    11·1 answer
  • Find the cartesian product Ax B of the following sets a) A = {x:x=1,2,3},b{y:y=3-x}​
    13·1 answer
  • WORTH 100 POINTS
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!