00:01
So for this problem, the first thing that we want to do is figure out what are different possible two element samples are from our original sample space.
00:09
Particularly, we can find that this table or this image that i've generated here shows on the left our different two element samples.
00:19
And then on the right, we can see sort of lined up with the middle of the two samples is the sample mean corresponding to those samples.
00:29
So once we have that, we can generate our table of the different possible values of x -bar, which we'll find to be in order 19 .75, 20, 21 .97, 23 .65, 23 .65, 23 .9, and 25 .6.
00:48
And the probability of each x -bar value by just tallying up the number of times each x -bar value occurs, and then dividing that by 15, the total sample size, or the total size, or rather total number of samples, that is.
01:04
So that would be 2 over 15 for 19 .75, 1 over 15 for 20, 3 over 15 for 21 .7, 21 .95, or pardon me, 2 over 15 for 21 .95, 4 over 15 for 23 .65, 2 over 15 for 23 .9, and 1 over 15 for 25 .6.
01:26
Where i'll note that for part c we'll want to calculate the expected value here, which we just find by taking the sum of the probability of each result times that individual result value...