Suppose X is a Bernoulli random variable with parameter p, 0 < p < 1, and suppose that Y = X+ 2. Given Y, Z is distributed as a binomial random variable with parameters n = Y and p. Suppose Z is observed to be 0. What is the conditional probability that X = 1, [Select ] and what is the probability that X = 0, [Select ] ? Given this information about Z, what is your revised (or conditional) expectation of X? [Select ]

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A:

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A:

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A:

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A: