<![CDATA[This research aims to identify and explain the concepts, asymptotic properties, relationships and applications of four types of convergence of a sequence of random variable, namely convergence almost surely, convergence in probability, convergence in distribution and convergence in mean. The results of the theoretical study shows that these four types of convergence, are closed to arithmetic operations, each subsequence is convergent to the same random variable, remains convergent in the continuous function,and has a relationship between each type, namely: (a) if the sequence of random variable convergent almost surely then this sequence convergent in probability and otherwise if the sequence has a subsequence that convergent almost surely to its limit, (b) if the sequence of random variable convergent in probability then this sequence convergent in distribution and otherwise if the limit is a real constant, (c) if the sequence of random variable convergent in mean then this sequence convergent in probability and otherwise if thesequence is bounded in probability and (d) there is no relationship between convergent in mean and convergent almost surely, and also can be used in proving the Law of Large Number, Central Limit Theorem and limit distribution.]]>
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