 Solution

ID: past-exam-of-the-probability-statistics-and-options-i-course-of-the-university-of-oxford/2010/o/3/a/solution

H_{0} : θ_{ij} = r_{i} c_{j}, \sum_{i = 1}^{2} r_{i} = \sum_{j = 1}^{3} c_{j} = 1.

The row distribution has one free parameter and the column distribution two, giving three free parameters under $H_{0}$ . Under the unrestricted alternative, six cell probabilities sum to one, giving five free parameters under $H_{1}$ . The difference is two, which is the degrees of freedom of the resulting chi-squared test.

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