Solution Found!
In Exercise 6.1, we considered a random variable Y with
Chapter 6, Problem 23E(choose chapter or problem)
In Exercise 6.1, we considered a random variable Y with probability density function given by
\(f(y)=\left\{\begin{array}{ll} 2(1-y), & 0 \leq y \leq 1 \\ 0, & \text { elsewhere, } \end{array}\right.\)
and used the method of distribution functions to find the density functions of
a \(U_{1}=2 \mathrm{Y}-1\).
b \(U_{2}=1-2 \mathrm{Y}\) .
c \(U_{3}=Y^{2}\).
Equation Transcription:
{
Text Transcription
F(y)= {2(1-y), 0 \leq y \leq 1 0 , elsewhere
U_1=2Y-1
U_2=1-2Y
U_3=Y^2
Questions & Answers
QUESTION:
In Exercise 6.1, we considered a random variable Y with probability density function given by
\(f(y)=\left\{\begin{array}{ll} 2(1-y), & 0 \leq y \leq 1 \\ 0, & \text { elsewhere, } \end{array}\right.\)
and used the method of distribution functions to find the density functions of
a \(U_{1}=2 \mathrm{Y}-1\).
b \(U_{2}=1-2 \mathrm{Y}\) .
c \(U_{3}=Y^{2}\).
Equation Transcription:
{
Text Transcription
F(y)= {2(1-y), 0 \leq y \leq 1 0 , elsewhere
U_1=2Y-1
U_2=1-2Y
U_3=Y^2
ANSWER:
Answer:
Step 1 of 3:
(a)
We considered a random variable with probability density function given by
And used the method of distribution functions to find the density function of
Use the method of transformation to find the densities of ,
.
The transformation method:
Let where
is either an increasing or decreasing function of
for all
such that
Step 1: We will find the inverse function,