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LECTURE NOTES 7 1 Stochastic convergence - stat.cmu.edu

LECTURE NOTES 71 Stochastic convergenceStochastic convergence refers to convergence of sequences of random variables. Recall fromthe last NOTES that we are concerned with two types of convergence in probability and con-vergence in distribution. convergence in probability implies convergence in distribution butthe reverse is not, in general, N(0,n 1) forn= 1,2,.. ThenYnP 0. We also have thatYn ZwhereZisdegenerate at 0, that isP(Z= 0) = 1. Also, nYn N(0,1). In fact, a stronger statementis true: nYnd=N(0,1) for suppose thatYn N(n,1).

LECTURE NOTES 7 1 Stochastic convergence Stochastic convergence refers to convergence of sequences of random variables. Recall from the last notes that we are concerned with two types of convergence in probability and con-

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Transcription of LECTURE NOTES 7 1 Stochastic convergence - stat.cmu.edu

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