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Unformatted text preview: n is called the partial sum process. Theorem 17.1 E | X i | < and let = E X i . Then S n n . This is known as the strong law of large numbers (SLLN). The convergence here means that S n ( ) /n for every S , where S is the probability space, except possibly for a set of of probability 0. The proof of Theorem 13.1 is quite hard, and we prove a weaker version, the weak law of large numbers (WLLN). The WLLN states that for every a > 0, P S n n-E X 1 > a as n . It is not even that easy to give an example of random variables that satisfy the WLLN but not the SLLN. Before proving the WLLN, we need an inequality called Chebyshevs in-equality. 42...
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This note was uploaded on 12/29/2011 for the course MATH 316 taught by Professor Ansan during the Spring '10 term at SUNY Stony Brook.
- Spring '10