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中文摘要：
概率密度函数连续的随机变量仅是一类特殊的连续型随机变量，因此假设概率密度函数连续是一个苛刻的限制．本文在随机变量概率密度函数连续和不连续两种不同假设下比较了两个典型例题的证明，可以看出两者的思路是完全不同的，后者通常更具有普遍性．
英文摘要：
The random variable with continuous probability density function is only a special kind of continuous random variables, so the assumption that random variable has a continuous probability density function is very strict. In this paper, we give a comparison of the proofs for two typical examples under continuous and discontinuous assumptions, it shows that these two methods are completely different, the latter usually has more universality.
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