Example 411 let the population consist of the numbers 12345...

EXAMPLE 4.1.1 Let the population consist of the numbers (1, 2, 3, 4, 5). Consider all possible samples consisting of three numbers randomly chosen without replacement from this population. Obtain the distribution of the sample mean. Solution: Disregarding the order, it is clear that there are 10 equally likely possible samples of size 3. They are (1, 2, 3), (1, 2, 4), (1, 2, 5), (1, 3, 4), (1, 3, 5), (1, 4, 5), (2, 3, 4), (2, 3, 5), (2, 4, 5), and (3, 4, 5). Calculating the mean, X, for each of the samples, we will get the sampling distribution of X.

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Transcript

00:01 Let the population consist of the numbers of 1 through 5.

00:04 Consider all possible samples consisting of three numbers randomly chosen.

00:09 So they list these numbers down at the bottom.

00:11 We have the set of 1, 2, 3, the set of 1, 2, 4, the set of 1, 2, 5, the set of 1, 3, 4, the set of 1, 3, 5, the set of 1, 3, 5, the set of 1, 4, 5, the set of 1, 4, 5, 5, the set of 1, 4, 5, 5, 5, 5.

00:34 3, 4, 2, 3, 5, 2, 4, 5, and 3, 4, 5.

00:49 To get the distribution of the sample mean, we need to find the main of each one of these samples.

00:57 So that means we're going to add them all together and divide by 3.

01:00 So this is going to end up being 6 divided by 3 or 2.

01:05 This is going to end up being 7 divided by 3.

01:08 This is going to end up being an 8 divided by 3.

01:12 This will end up being 8 divided by 3.

01:14 This is going to end up 9 divided by 3, which is 3.

01:18 This will be 10 over 3.

01:20 That's going to be 9 over 3, which is 3.

01:25 That's going to be 10 over 3.

01:27 That's going to end up being 11 over 3.