Solution Found!
If n > 2 is an integer, the distribution with density
Chapter 4, Problem 189SE(choose chapter or problem)
If \(n>2\) is an integer, the distribution with density given by
\(f(y)=\left\{\begin{array}{ll}
\frac{1}{B(1 / 2,[n-2] / 2)}\left(1-y^{2}\right)^{(n-4) / 2}, & -1 \leq y \leq 1, \\
0, & \text { elsewhere. }
\end{array}\right.
\)
is called the 𝑟 distribution. Derive the mean and variance of a random variable with the 𝑟 distribution.
Equation Transcription:
Text Transcription:
n>2
f(y)=
1 over B(1/2, [n-2]/2) (1-y^2)^(n-4)/2, -1</=y</=1,
0, elsewhere.
Questions & Answers
QUESTION:
If \(n>2\) is an integer, the distribution with density given by
\(f(y)=\left\{\begin{array}{ll}
\frac{1}{B(1 / 2,[n-2] / 2)}\left(1-y^{2}\right)^{(n-4) / 2}, & -1 \leq y \leq 1, \\
0, & \text { elsewhere. }
\end{array}\right.
\)
is called the 𝑟 distribution. Derive the mean and variance of a random variable with the 𝑟 distribution.
Equation Transcription:
Text Transcription:
n>2
f(y)=
1 over B(1/2, [n-2]/2) (1-y^2)^(n-4)/2, -1</=y</=1,
0, elsewhere.
ANSWER:
Solution:
Step 1 of 3:
If n>2 is an integer, the distribution with density given by
Which is called r distribution.
We have to derive the mean and variance of r distribution.