We have m independent identically distributed (iid) observations {y1, ., ym}, from a negative binomial distribution: frie(y) = y - 1 er ( 1 - 0 ) 3-...

5. We have m independent identically distributed (iid) observations {y1, ..., ym}, from anegative binomial distribution:frie(y) =y - 1er ( 1 - 0 ) 3- for y = r,r+ 1,r+ 2, ...with a known value r and an unknown parameter 0 (0 < 0 < 1). Suppose that theparameter 0 has the prior pdf given by: 605 for 0 < 0 < 1 which is a Beta(6,1) prior.(a) Find the posterior distribution of 0.(b) Compute the Bayes estimate for 0.(c) Compute the Bayes estimate for 0(1 - 0)2.(5+5+5=15)