1. Suppose that a list contains the values 20 44 48 55 62 66 74 88 93 99 at index positions 0 through 9. Trace the values of the variables….

## Show that if H is PAC learnable (in the standard one-oracle model), then H is PAC learnable in the two-oracle model.

1. (*) Show that if *H *is PAC learnable (in the standard one-oracle model), then *H *is PAC learnable in the two-oracle model.

2. (**) Define *h*+ to be the always-plus hypothesis and *h*− to be the always-minus hypothesis. Assume that *h*+ *,**h*− ∈ *H*. Show that if *H *is PAC learnable in the two-oracle model, then *H *is PAC learnable in the standard one-oracle model.

3.1 In this exercise, we show that the (*_, δ*) requirement on the convergence of errors in our definitions of PAC learning, is, in fact, quite close to a simpler looking requirement about averages (or expectations). Prove that the following two statements are equivalent (for any learning algorithm *A*, any probability distribution *D*, and any loss function whose range is [0*, *1]):