The natural logarithm base e is typically used in the context of continuous probability distributions, such as the Weibull, Poisson, and Normal distributions. For the Weibull distribution, the scale parameter often involves the natural logarithm. The Poisson distribution's probability mass function frequently involves the exponential function, which is based on e. The Normal distribution's density function also contains e. However, the Binomial distribution does not inherently require the base e for its probability calculations, as it involves factorials and combinations without the necessity of natural logarithms.