1. Atwo-pole 60 Hz induction motor has a slip of2%on full load. The full-load speed is (a) 58.8 r/s (b) 3528 r/min (c) 60 r/s (d) 2880 r/min 2.The….

## Show that for every probability distribution D, the Bayes optimal predictor fD is optimal, in the sense that for every classifier g from X to {0,1}, LD( fD) ≤ LD(g).

1. Let *H *be a hypothesis class of binary classifiers. Show that if *H *is agnostic PAC learnable, then *H*is PAC learnable as well. Furthermore, if *A *is a successful agnostic PAC learner for *H*, then *A *is also a successful PAC learner for *H*.

2. (*) The Bayes optimal predictor: Show that for every probability distribution *D*, the Bayes optimal predictor *fD *is optimal, in the sense that for every classifier *g *from *X *to {0*,*1}, *LD*( *fD*) ≤ *LD*(*g*).

3. (*) We say that a learning algorithm *A is better than B with respect to *some probability distribution, *D*, if

*LD*(*A*(*S*))≤ *LD*(*B*(*S*)) for all samples *S *∈ (*X *×{0*,*1})*m*.We say that a learning algorithm *A is better than B*, if it is better than *B *with respect to all probability distributions *D *over *X *×{0*,*1}.