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l. (6 points) Assume p with 0

I. (6 points) Assume p with O < p < I is a random variable with a uniform distribution. Assume that the random variables Xl,X2,... , are independent given p, that they can have either O or I as their value, and that given p, the probability for I is p. (a) What is the marginal probability that = 1? (b) Assume that you have observed = l, x2 = 0, .x3 = 0. What is the probability distribution for p given this data? (c) Given that you have observed = 1, x2 = 0, and x3 = 0, what is the probability that