To find the variance of a hypergeometric random variable

Chapter 2, Problem 10E

(choose chapter or problem)

Get Unlimited 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

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,


Add to cart


Study Tools You Might Need

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back