∙WhenWn:n1,2,...,nconverges in probability tocwe also saythatcis theprobability limitofWn. Sometimes we get sloppy andrefer toWn, but convergence in probability is aboutsequencesofrandom variables.∙More notation. We writeplimn→Wnc(and often drop “n→”) orWnp→c15
∙There is an important notation for the special caseWnp→0. As wewill see later, to facilitate the alebra of asymptotic theory, it is handy towriteWnop1(read “little oh pee one”) whenWnp→0. We will seein Section 4 where the “1” in parentheses comes from.∙The definition extends immediately to the idea of convergence inprobability to a random variable rather than a constant (although itcomes up less often). We require, for all0,P|Wn−W|≥→0 asn→.16
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