8. (a) Let X X Xn
, , , 1 2 K be independently and identically distributed b ,1( p) random
variables. Obtain a confidence internal for p using Chebychev’s inequality.
For sample mean
X‾=1N∑xk\overline{X}=\frac{1}{N}\sum x_kX=N1∑xk
using Chebishev inequality:
P(∣X‾−μ∣≥b)≤σ2Nb2P(|\overline{X}-\mu|\geq b)\leq\frac{\sigma^2}{Nb^2}P(∣X−μ∣≥b)≤Nb2σ2
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