g Quantifying Consistency 1 point possible (graded) Note: The problem statement has been changed to asking about convergence in probability instead of almost surely. Attempts will be reset. Let X1,…,Xn∼iidBer(p). Let X¯¯¯¯n be the estimator given by 1n∑i=1nXi. What is the smallest constant c such that nc(X¯¯¯¯n−p)=nc(1n∑i=1nXi−p) does not converge to 0 in probability as n→[infinity]?

Out of five men and five women, we form a committee consisting of four different people. assuming that each committee of size four is equally likely, find the probabilities of the following events: 1. the committee consists of two men and two women 2. the committee has more women than men. 3. the committee has at least one man. for the remainder of the problem assume that alice and bob are among the ten people being considered. 4. both alice and bob are members of the committee.