 Solution

ID: past-exam-of-the-options-ii-course-of-the-university-of-oxford/2012/m/m4/a/i/solution

Each ticket is equally likely, so the supplied sums give

E X = \frac{40}{10} = 4, E X^{2} = \frac{216}{10} = \frac{108}{5} .

Hence

E X = 4, Var (X) = E X^{2} - (E X)^{2} = \frac{28}{5} = 5.6.

Repeated numerical values still represent different equally likely tickets; they must retain their multiplicities.

 New to topics? Read the docs here!