Solution Found!
To find the variance of a hypergeometric random variable
Chapter 2, Problem 10E(choose chapter or problem)
To find the variance of a hypergeometric random variable in Example 2.3-4 we used the fact that
\(E[X(X-1)]=\frac{N_{1}\left(N_{1}-1\right)(n)(n-1)}{N(N-1)}\) .
Prove this result by making the change of variables \(k=x-2\) and noting that
\(\left(\begin{array}{l}N \\n\end{array}\right)=\frac{N(N-1)}{n(n-1)}\left(\begin{array}{c}N-2 \\ n-2\end{array}\right)\).
Equation Transcription:
Text Transcription:
E[X(X-1)]=N_1(N_1-1)(n)(n-1)/N(N-1)
k=x-2
(_n^N)=N(N-1)/n(n-1)N-2 n-2
Questions & Answers
QUESTION:
To find the variance of a hypergeometric random variable in Example 2.3-4 we used the fact that
\(E[X(X-1)]=\frac{N_{1}\left(N_{1}-1\right)(n)(n-1)}{N(N-1)}\) .
Prove this result by making the change of variables \(k=x-2\) and noting that
\(\left(\begin{array}{l}N \\n\end{array}\right)=\frac{N(N-1)}{n(n-1)}\left(\begin{array}{c}N-2 \\ n-2\end{array}\right)\).
Equation Transcription:
Text Transcription:
E[X(X-1)]=N_1(N_1-1)(n)(n-1)/N(N-1)
k=x-2
(_n^N)=N(N-1)/n(n-1)N-2 n-2
ANSWER:
Answer:
Step 1 of 3:
To find the variance of a hypergeometric random variable.
Let X be the hypergeometric distribution.
Here, n selected from N =
n = x + (n - x) , where ‘x’ selected from and (n - x) selected from .
Therefore,
Then ,
E(X) = =
=
=
Therefore,