Fundamental methods are developed for the derivation of the probability density function and moments of rational algebraic functions of independent random variables. Laplace and Mellin integral ...

Random Variable: A measurable function that maps outcomes in a probability space to real numbers, thereby enabling quantitative analysis of random events.

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.

Luc Devroye, Gábor Lugosi, Local Tail Bounds for Functions of Independent Random Variables, The Annals of Probability, Vol. 36, No. 1 (Jan., 2008), pp. 143-159 ...

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

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 ...

Sample space and events, probability measure and probability space, random variable as a measurable function, distribution function of a random variable, discrete and continuous-type random ...