 Solution

ID: past-exam-of-the-probability-statistics-and-options-ii-course-of-the-university-of-oxford/2010/o/o4/b/ii/solution

1, - 1

. Applying the joint central limit approximation from (i) gives

\overset{p}{^} - \overset{q}{^} \approx N (p - q, \frac{p ( 1 - p )}{2 M} + \frac{q ( 1 - q )}{2 N}) .

Equivalently the difference minus

p - q

, divided by the displayed standard deviation, converges in distribution to a standard normal under the same regular large-sample regime.

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