Given X₁, ..., X, are n independent identically distributed samples of random variable X with PMF x = 0, x = 1, otherwis
Posted: Wed Jul 06, 2022 12:27 pm
- Given X X Are N Independent Identically Distributed Samples Of Random Variable X With Pmf X 0 X 1 Otherwis 1 (34.21 KiB) Viewed 12 times
Given X₁, ..., X, are n independent identically distributed samples of random variable X with PMF x = 0, x = 1, otherwise. (0.1 Px(x) = 0.9 0 a) Determine how is E[X] related to Px (1). b) Use Chebyshev's inequality to find the confidence level x 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 (1)| ≥ 0.05] ≤ a c) Use Chebyshev's inequality to find out how many samples n are necessary to have M₁, (X) within 0.03 of Px (1) with confidence level 0.1. In other words, find n such that P[|Mn(X) - Px (1)| ≥ 0.03] ≤ 0.1.