Problem $1.$

A$.$ Suppose we have a hypothesis whose true error is $\mathrm{.}1.$ Give upper bounds on the probability that if we draw a random sample of size n$,$ we observe an empirical error of at least $\mathrm{.}2.$ Use Hoeffding and Chernoff. Which is better for large n$?$

B$.$ Now do the same with true error $\mathrm{.}4$ and empirical error $\mathrm{.}5.$ Compare with part A and explain the results.