Probability | Part IA, 2008

The discrete random variable YY has distribution given by

P(Y=k)=(1p)k1p,k=1,2,\mathbb{P}(Y=k)=(1-p)^{k-1} p, \quad k=1,2, \ldots

where p(0,1)p \in(0,1). Determine the mean and variance of YY.

A fair die is rolled until all 6 scores have occurred. Find the mean and standard deviation of the number of rolls required.

[Hint: i=16(6i)2=53.7]\left.\sum_{i=1}^{6}\left(\frac{6}{i}\right)^{2}=53.7\right]

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