Recent content by jumpr

Homework Statement Let x be the number of successes in n independent Bernoulli trials, each one having unknown probability θ of success. Assume θ has prior distribution θ ~ Unif(0,1). An extra trial, z, is performed, independent of the first n given θ, but with probability θ/2 of success. Show...

Sorry, I'm going to have to ask for a hint as to where to go from there. My ideas for proofs tend to break down when I want to assume a_{i} \in H for some a_{i}when G = \mathbb{Z}a_{1} + ... + \mathbb{Z}a_{n}.

Does this work? Let K \le H be finitely generated where H/K is finitely generated, say K = \mathbb{Z}a_{1} + ... + \mathbb{Z}a_{n} and H/K = \mathbb{Z}(b_{1} + K) + ... + \mathbb{Z}(b_{m} + K) = \mathbb{Z}b_{1} + ... + \mathbb{Z}b_{m} + K, where the b_{i} \in H. Let h \in H, and consider h +...

Homework Statement Prove that any subgroup of a finitely generated abelian group is finitely generated. Homework Equations The Attempt at a Solution I've attempted a proof by induction on the number of generators. The case n=1 corresponds to a cyclic group, and any subgroup of a...