Refer to Exercise 3.115. Find ?, the expected value of Y,

Chapter 3, Problem 190SE

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QUESTION:

Refer to Exercise 3.115. Find , the expected value of Y , for the theoretical population by using the probability distribution obtained in Exercise 3.115. Find the sample mean  for the  = 100 measurements generated in Exercise 3.116. Does \(\bar{y}\) provide a good estimate of \(\mu)?

Equation transcription:

Text transcription:

bar{y}

mu

Questions & Answers

QUESTION:

Refer to Exercise 3.115. Find , the expected value of Y , for the theoretical population by using the probability distribution obtained in Exercise 3.115. Find the sample mean  for the  = 100 measurements generated in Exercise 3.116. Does \(\bar{y}\) provide a good estimate of \(\mu)?

Equation transcription:

Text transcription:

bar{y}

mu

ANSWER:

Solution

Step 1 of 2

We have to find  and we have to prove that weather  provides a good estimate of

The pmf of hyper geometric distribution is

Here N=population size=6

          n=sample size=3

          r=no.of success=2

Then

         

           

Now =E(Y)

            =

            =0(0.2)+1(0.6)+2(0.2)

            =1


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