It includes discrete and continuous random variables, their probability distributions and analytical and statistical methods for determining the mean, variance and higher order moments that ...

Probability Density Function (PDF): For a continuous random variable, a function f (x) whose integral over any interval yields the probability that the variable falls within that interval.

The world is full of uncertainty: accidents, storms, unruly financial markets, noisy communications. The world is also full of data. Build foundational knowledge of data science with this introduction ...

Probability, statistics, reliability and decision with applications in engineering. Probability of events, discrete and continuous random variables, probability density functions and distributions, ...

We propose a flexible method to approximate the subjective cumulative distribution function of an economic agent about the future realization of a continuous random variable. The method can closely ...

As applications we derive necessary and sufficient conditions for a sequence of probability measures to be the sequence of distributions of a martingale (Theorem 8), an upper semi-martingale (Theorem ...