1ft X1,...,Xn are n independent identically distributed samples of random variable X with PMF

(a) How is E[X) related to Px(l)?
(b) Use Chebyshev's inequality to find the confidence level a such that M90(X), the estimate based on 90 observations, is within 0.05 of PX(1). In other words, find a such that
P [|M90(X) - Px(l)| ‰¥ 0.05] ‰¤ a.
(c) Use Chebyshev's inequality to find out how many samples n are necessary to have Mn(X) within 0.03 of PX(l) with confidence level 0.1. In other words, find n such that
P [|Mn(X) - Px(1)| ‰¥ 0.03] ‰¤ 0.1.

Transcribed Image Text:

0.1 0.9 0 otherwise. x=0, Px(x)= x=1,