Consider an urn containing black and white balls. The probability of drawing a black ball is...

 

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Consider an urn containing black and white balls. The probability of drawing a black ball is p which is unknown. Assume that p has a prior distribution which is uniform(0, 1). We repeatedly draw balls with replacement. (a) Obtain the posterior distribution of p after observing a - 1 black balls and 3-1 white balls. (b) What is the posterior mean of p? (c) If a = 3 and B = 1, obtain a 95% credible interval estimate for p. Interpret the interval. Consider an urn containing black and white balls. The probability of drawing a black ball is p which is unknown. Assume that p has a prior distribution which is uniform(0, 1). We repeatedly draw balls with replacement. (a) Obtain the posterior distribution of p after observing a - 1 black balls and 3-1 white balls. (b) What is the posterior mean of p? (c) If a = 3 and B = 1, obtain a 95% credible interval estimate for p. Interpret the interval.