Mean and Variance:

The mean and variance are measures of central tendency and dispersion, respectively, in a set of data. The mean represents the average value of the observations, while variance measures the spread or dispersion of the data points around the mean.

Given Information:

In this case, we are given that the mean of five observations is 4.4 and the variance is 8.24. Additionally, we are provided with three of the observations, which are 1, 2, and 6. We need to find the other two observations.

Calculating the Mean:

To calculate the mean, we add up all the observations and divide the sum by the total number of observations. In this case, the sum of the five observations is (1 + 2 + 6 + x + y), where x and y are the unknown observations. We know that the mean is 4.4, so we can set up the equation:

(1 + 2 + 6 + x + y)/5 = 4.4

Simplifying the equation, we get:

9 + x + y = 22

x + y = 13

Calculating the Variance:

To calculate the variance, we need to find the squared deviations of each observation from the mean, sum them up, and divide by the total number of observations. However, since we only have the variance value, we can use the formula for variance to solve for the sum of the squared deviations. The formula for variance is:

Variance = (sum of squared deviations)/n

Given that the variance is 8.24 and the total number of observations is 5, we can set up the equation:

8.24 = ([(1-4.4)^2 + (2-4.4)^2 + (6-4.4)^2 + (x-4.4)^2 + (y-4.4)^2])/5

Simplifying the equation, we get:

8.24 = ((-3.4)^2 + (-2.4)^2 + (1.6)^2 + (x-4.4)^2 + (y-4.4)^2)/5

8.24 = 11.56 + 5.76 + 2.56 + (x-4.4)^2 + (y-4.4)^2

8.24 = 20.88 + (x-4.4)^2 + (y-4.4)^2

(x-4.4)^2 + (y-4.4)^2 = 8.24 - 20.88

(x-4.4)^2 + (y-4.4)^2 = -12.64

Since the sum of squares cannot be negative, it is not possible to find real values for x and y that satisfy this equation. Therefore, there are no other valid observations that can satisfy the given mean and variance conditions.

In conclusion, based on the given mean and variance, and the three known observations, it is not possible to determine the other two observations.