STAT 830 Convergence in Distribution - People.stat.sfu.ca - Simon ...
STAT 830 Convergence in Distribution - People.stat.sfu.ca - Simon ...
STAT 830 Convergence in Distribution - People.stat.sfu.ca - Simon ...
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Some numeri<strong>ca</strong>l examples?Answers depend on how close close needs to be so it’s a matter ofdef<strong>in</strong>ition.In practice the usual sort of approximation we want to make is to saythat some random variable X, say, has nearly some cont<strong>in</strong>uousdistribution, like N(0,1).So: want to know probabilities like P(X > x) are nearlyP(N(0,1) > x).Real difficulty: <strong>ca</strong>se of discrete random variables or <strong>in</strong>f<strong>in</strong>itedimensions: not done <strong>in</strong> this course.Mathematicians’ mean<strong>in</strong>g of close: Either they <strong>ca</strong>n provide an upperbound on the distance between the two th<strong>in</strong>gs or they are talk<strong>in</strong>gabout tak<strong>in</strong>g a limit.In this course we take limits.Richard Lockhart (<strong>Simon</strong> Fraser University) <strong>STAT</strong> <strong>830</strong> <strong>Convergence</strong> <strong>in</strong> <strong>Distribution</strong> <strong>STAT</strong> <strong>830</strong> — Fall 2011 5 / 31
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