20.21. Suppose that the sequence (X) is fundamental in probability in the sense that for e positive there exists an N such that P[IX-X|>e] N. (a) Prove there is a subsequence (X) and a random variable X such that lim XX with probability 1. Hint: Choose increasing n such that P[IX-X|>2-k]<2-k for m, n ≥n. Analyze P[IX-Xn₂>2-k]. (b) Show that X,₁ →p X.

20.21. Suppose that the sequence (X) is fundamental in probability in the sense that for e positive there exists an N such that P[IX-X|>e] N. (a) Prove there is a subsequence (X) and a random variable X such that lim XX with probability 1. Hint: Choose increasing n such that P[IX-X|>2-k]<2-k for m, n ≥n. Analyze P[IX-Xn₂>2-k]. (b) Show that X,₁ →p X.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.7: Introduction To Coding Theory (optional)

Problem 6E: Suppose the probability of erroneously transmitting a single digit is P=0.03. Compute the...

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