Discuss the proposition of the Hermite polynomial when the independent variable is a random variable, and discuss some random variables in the same distribution are convergence in probability.

• 摘要讨论当埃尔米特多项式中的自变量是随机变量时所具有的性质，以及一列同分布的随机变量乘积和依概率收敛于埃尔米特多项式。