Solution Found!
A member of the power family of distributions has a
Chapter 6, Problem 17E(choose chapter or problem)
A member of the power family of distributions has a distribution function given by
\(F(y)=\left\{\begin{array}{ll} 0, & y<0 \\ \left(\frac{y}{\theta}\right)^{n}, & 0 \leq y \leq \theta \\
1, & y>\theta \end{array}\right.\)
where \(\alpha, \theta>0\).
a Find the density function.
b For fixed values of \(\alpha \text { and } \theta\), find a transformation so that
has a distribution function of
when
possesses a uniform
distribution.
C Given that a random sample of size 5 from a uniform distribution on the interval yielded the values
, and 3609 , use the transformation derived in part (b) to give values associated with a random variable with a power family distribution with \(\alpha=2, \theta=4\).
Equation Transcription:
{
Text Transcription:
f(y) = {0, y<0 (y over \theta )n 0 \leq y \leq \theta 1, y > \theta
\alpha, \theta>0
\alpha and \theta
\alpha=2, \theta=4
Questions & Answers
QUESTION:
A member of the power family of distributions has a distribution function given by
\(F(y)=\left\{\begin{array}{ll} 0, & y<0 \\ \left(\frac{y}{\theta}\right)^{n}, & 0 \leq y \leq \theta \\
1, & y>\theta \end{array}\right.\)
where \(\alpha, \theta>0\).
a Find the density function.
b For fixed values of \(\alpha \text { and } \theta\), find a transformation so that
has a distribution function of
when
possesses a uniform
distribution.
C Given that a random sample of size 5 from a uniform distribution on the interval yielded the values
, and 3609 , use the transformation derived in part (b) to give values associated with a random variable with a power family distribution with \(\alpha=2, \theta=4\).
Equation Transcription:
{
Text Transcription:
f(y) = {0, y<0 (y over \theta )n 0 \leq y \leq \theta 1, y > \theta
\alpha, \theta>0
\alpha and \theta
\alpha=2, \theta=4
ANSWER:Solution:
Step 1 of 3:
A member of the power family of distributions has a distribution
Where,
- The claim is to find the density function
The density function is f(y) =
= , 0
Hence, the density function is f(y) =