Final answer:
The variance of the difference can be found by adding the variances, 0.5 and 14 .The distribution of x1 + x2 is N(10, 2.055) and the distribution of x1 - x2 is N(-6, 16.77).
Step-by-step explanation:
The distribution of the sum of two normally distributed variables is also normally distributed.
Therefore, the distribution of x1 + x2 will also be a normal distribution.
The mean of the sum can be found by adding the means, 2 and 8, which gives 10.
The variance of the sum can be found by adding the variances, 0.5 and 14, and multiplying by the square of the correlation coefficient, which gives (0.5 + 14) * (-0.3)^2 = 2.055.
Therefore, the distribution of x1 + x2 is N(10, 2.055).
The distribution of the difference of two normally distributed variables is also normally distributed.
Therefore, the distribution of x1 - x2 will also be a normal distribution.
The mean of the difference can be found by subtracting the means, 2 and 8, which gives -6.
The variance of the difference can be found by adding the variances, 0.5 and 14, and subtracting twice the product of the standard deviations and the correlation coefficient, which gives (0.5 + 14) - 2 * sqrt(0.5) * sqrt(14) * (-0.3) = 16.77.
Therefore, the distribution of x1 - x2 is N(-6, 16.77)