Sample size to distinguish Bernoulli from Uniform distribution

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I would like to address the following question. How many samples is required to distinguish between a Bernoulli distribution with parameter $1/2 - \epsilon$ and a uniform distribution over $\{0, 1\}$. I know that this statement is not mathematically rigorous, so I'm looking to answer two questions:

  1. How can I rephrase the statement to be mathematically rigorous?
  2. I feel like somehow concentration measures (like Hoeffding's inequality) may help to answer the question, but don't know how, any idea?