00:01
In this problem, we are given a table that shows the values of a function are and its three unit moving averages are bar for different values of x.
00:19
We are asked to complete the table by filling in the missing values.
00:23
So first consider the table given.
00:26
This is the table of values given with x values, r of x values.
00:31
And r bar of x values.
00:33
We can reconstruct this table.
00:36
This is the table reconstructed and the blanks has to be filled.
00:41
Now we have by definition the three point moving average r bar of x is obtained by summing three terms at a time which are consecutive terms and dividing the sum by three.
00:54
So the first three unit moving average r bar of two is obtained as.
01:02
R of zero plus r of one plus r of two which are the first three consecutive terms divided by three so first blank that has to be filled is for r of two so from the table we know that r of r bar of two is seven so we have seven is equal to r of zero is given to be six plus r of one is given to be four plus r of two has to be determined divided by three so from here we get 21 is equal to 10 plus r of 2 that is we get the value of r of 2 to be 21 minus 10 which is 11 this is the first required answer so here we can fill in 11 next we need r of 3 we are given our bar of 3 as 6 so we have 6 is equal to r of 1 plus r of 2 plus r of 3 divided by 3 which is the second 3 unit moving average.
02:04
So we have 18 is equal to r of 1 is 4 plus r of 2 is evaluated to be 11 plus r of 3...