 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2014/discrete-mathematics-continuous-mathematics-and-probability/9/b/ii/solution

Let

X_{i}

i

1/2

, so

μ = 1/2

σ = 1/2

, and

W = N / n

. Taking

h = 1/5

makes

hσ = 1/10

. The preceding Chebyshev's inequality bound gives

P (0.4 \leq \frac{N}{n} \leq 0.6) \geq 1 - \frac{25}{n} \geq \frac{3}{4}, n \geq 100.

The endpoints are included because this event is exactly

∣ W - 1/2∣ \leq 1/10

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