Find an interval I𝜃 (that depends on 𝜃 ) centered about 𝑋⎯⎯⎯⎯⎯𝑛 such that

Question

𝐏(I𝜃∋𝜃)=0.9for all 𝑛(i.e, not only for large 𝑛).

(Write barX_n for 𝑋⎯⎯⎯⎯⎯𝑛 . Use the estimate 𝑞0.05≈1.6448 for best results.)

I𝜃=[𝐴𝜃,𝐵𝜃] for

𝐴𝜃 =

𝐵𝜃 =

Answer 1

1. TRUE

2. mean = theta
variance = theta/n