Question

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. 

Answer 1

For sample mean

$\overline{X}=\frac{1}{N}\sum x_k$

using Chebishev inequality:

$P(|\overline{X}-\mu|\geq b)\leq\frac{\sigma^2}{Nb^2}$