Final answer:
The sum of the other two observations is 13. However, it is not possible to find two observations that satisfy the given conditions.
Step-by-step explanation:
To find the other two observations, we can use the given mean and variance to calculate the sum of all five observations. Given that the mean of the five observations is 4.4, the sum of all five observations can be found by multiplying the mean by 5, which gives us 22. Then, subtract the sum of the three given observations (1+2+6) which is 9, to get the sum of the other two observations. The sum of the other two observations is 22 - 9 = 13.
Since the variance is given as 8.24, we can use the formula for variance to find the sum of the squares of the five observations. The formula for variance is sum of the squares / n - mean squared. We can rearrange this formula to find the sum of the squares, which is equal to the variance times n - mean squared. Plugging in the values, we get 8.24 * (5 - 4.4)^2 = 4.968. Now, we know that the sum of the squares of the three given observations is 1^2 + 2^2 + 6^2 = 41.
To find the sum of the squares of the other two observations, we subtract the sum of the squares of the three given observations from the total sum of squares. The sum of the squares of the other two observations is 4.968 - 41 = -36.032. Since we cannot have negative numbers as observations, we can conclude that it is not possible to find two observations that satisfy the given conditions.