$1)$ Assume that you are given a MDP with finite number of states.a$.$ Is Value iteration guaranteed to converge if the discount factor $()$ satisfies $0<<1?$ Explain.b$.$ Are policies found by value iteration superior to policies found by policy iteration?Explain.

$2)$ What is the difference between a Reward and a Value for a given State?

$3)$ It is known that Q$-$learning is an instance of off$-$policy learning method because the updated policy is different from the policy that agent follows. Can Q$-$learning learn the optimal Q$-$ function Q without ever executing the optimal policy? Please explain.