4. Let X₁, X₂, ..., Xn denote a random sample from a geometric distribution with success probability p (0 < p < 1) and d
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4. Let X₁, X₂, ..., Xn denote a random sample from a geometric distribution with success probability p (0 < p < 1) and defined by: p(x\p) = {p (1 − p)¹-x Use the conjugate beta (a, B) prior for p to do the following a) Compute the joint likelihood: f(x₁,x2,..., xn, p) = L(x₁,x2,...,xn|p) × g (p). b) Compute the marginal mass function: x = 1,2,..., n otherwise 00 m(x1,x2,...,xn) = [ L(x1,x2,..., Xn\p) × g(p) dp. -00 c) Compute the posterior density: g* (p|x₁,x₂,...,xn) = L(x₁,x2,...,xn|p) x g(p) dp SL(x₁,x₂,...,xn|p) × g (p) dp (10 marks) (6 marks) (12 marks)