Chapter 7 7.4

page 74

Could the following part of the proof be made clearer. In my case I don't follow the final manipulating of the equations (3rd to 4th say)

|B_{n}(p) - f(p)| <= E(Y_{n})

= E(Y_{n};Z_{n} <= \delta ) + E(Y_{n} ; Z_{n} > \delta)

<= 1/2 \epsilon P (Z_{n} <= \delta ) + 2KP(Z_{n} > \delta)

<= 1/2 \epsilon + 2K/(4n \delta^{2} ) :: where does the the 2K/(4n \delta^{2} ) come from?!

"Earlier, we chose a fixed \delta at (a). We now choose n so that

2K/(4n \delta^{2} ) < 1/2 \epsilon

...."