 Solution

ID: past-exam-of-the-options-ii-course-of-the-university-of-oxford/2011/m/m4/b/v/solution

2^{T}

. On

{T \geq 5}

it is at least

32

, so

P (T \geq 5) \leq \frac{E ( 2 ^{T} )}{32} = \frac{7}{192} < 0.05.

This exponential bound is substantially stronger here than applying Markov inequality directly to

T

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