Question

three randomly selected households are surveyed. the numbers of people in the households are 1,3,8 assume that samples of size n =2 are randomly selelcted with replacement from the population of 1,3,8. Listed below are the nine different sampls

1,1 1,3 1,8 3,1 3,3 3,8 8,1 8,3 8,8


find the variance of each of the nine samples then summerize the sampling distribution of the variances in the format of a table representing the probability distribution of the distinct variance values


s^2 Probability

3.3

1

6.3

49

Answer 1

i have no clue how to do this

Answer 2

I know some statistics, but this problem is very confusing.

So I understand that 3 households are sampled.

Now, is the number in each of these households equal to 1, 3 and 8 people?

Next, the question says, samples of n=2 are randomly selected (with replacement) from these 3.

So are sample space is

11
13
31
33
18
81
38
88
83
88

This is done 9 times.

Is that how you understand the problem?

When they select the household with only 1 person, the variance is 0
When they select the household with 8 people, they variance will be from a discrete uniform distribution
Similarly for household with 3 individuals.

But to ask the variance of each sample is a mystery. Is it asking the variance of the population of each or of the group. It is very unclear to me.

I'm sorry.

Answer 3

its okay thank you i am having a hard time understanding it too thought i would ask

Answer 4

i thought the way it was done was 1-1divided by 2 1-3 divided by two and so fourth but the numbers dont add up

Answer 5

here is a similar question
We have the following cases to consider (1,1), (1,4), (1,10) ,(4,4) (4,10), (10,10). Well we know three of our samples will have a variance of 0. The variance for the case when we have 1 and 4 is 4.5; likewise, the variance for when we have 10 and 4 is 18 and the variance for when we have 1 and 10 is 40.5. The possible variances are 0, 4.5, 18, and 40.5. The probability of having a variance of 0 is 3/9. For a variance of 4.5 its 2/9, for 18 its 2/9 and lastly, for a variance of 40.5 its 2/9. As you can see, 3/9 + 2/9 + 2/9 + 2/9 = 1.