Probability | Part IA, 2008

A standard six-sided die is thrown. Calculate the mean and variance of the number shown.

The die is thrown nn times. By using Chebyshev's inequality, find an nn such that

P(Ynn3.5>1.5)0.1\mathbb{P}\left(\left|\frac{Y_{n}}{n}-3.5\right|>1.5\right) \leqslant 0.1

where YnY_{n} is the total of the numbers shown over the nn throws.

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