 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2013/discrete-mathematics-probability-and-continuous-mathematics/8/c/ii/solution

Part (a) with

n = 6

gives

E [S_{1}] = E [S_{2}] = 7/2

and

var (S_{1}) = var (S_{2}) = 35/12

E [X] = 7, E [Y] = 0.

var (- S_{2}) = var (S_{2})

give the same variance for the sum and difference:

E [X] = 7, E [Y] = 0, var (X) = var (Y) = \frac{35}{6} .

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