Here we will give an illustrative example of a weak learner for a simple concept class. Let the domain be the real line, R$,$ and let C refer to the concept class of $3-$piece classifiers$,$ which are functions of the following form: for $01<02$ and be$\{-1,1\},$ h$81,62,6($x$)$ is b if x $[01,02]$ and $$b otherwise. In other words, they take a certain Boolean value inside a certain interval and the opposite value everywhere else. For example, h$10,20,1($x$)$ would be $+1$ on $[10,20),$ and $-1$ everywhere else. Let H refer to the simpler class of $$decision stumps$,$ i$.$e$.$ functions ho$,6$ such that h$(2)$ is b for all x $<0$ and $-$b otherwise. $($a$)$ Show formally that for any distribution on R $($assume finite support, for simplicity; i$.$e$.,$ assume the distribution is bounded within $(-$B$,$ B$]$ for some large B$)$ and any unknown labeling function ce C that is a $3-$piece classifier, there exists a decision stump h E H that has error at most $1/3,$ i$.$e$.$ P$[$h$($x$)+$ c$($x$)]<1/3.($b$)$ Describe a simple, efficient procedure for finding a decision stump that minimizes error with respect to a finite training set of size m$.$ Such a procedure is called an empirical risk minimizer $($ERM$).($c$)$ Give a short intuitive explanation for why we should expect that we can easily pick m sufficiently large that the training error is a good approximation of the true error, i$.$e$.$ why we can ensure generalization.