Abstract: We derive the characteristic function (CF) for two product distributions—first for the product of two Gaussian random variables (RVs), where one has zero mean and unity variance, and the ...

The total area under the curve must equal 1, representing the fact that the probability of some outcome occurring within the entire range is certain. \[\int_{-\infty}^{\infty}f\left(x\right)dx=1\] ...

Investopedia contributors come from a range of backgrounds, and over 25 years there have been thousands of expert writers and editors who have contributed. Robert Kelly is managing director of XTS ...

The binomial distribution is a key concept in probability that models situations where you repeat the same experiment several times, and each time there are only two possible outcomes—success or ...

Will Kenton is an expert on the economy and investing laws and regulations. He previously held senior editorial roles at Investopedia and Kapitall Wire and holds a MA in Economics from The New School ...

A random variable is a mathematical function that maps outcomes of random experiments to numbers. It can be thought of as the numeric result of operating a non-deterministic mechanism or performing a ...

Stochastic gradient-based optimisation for discrete latent variable models is challenging due to the high variance of gradients. We introduce a variance reduction technique for score function ...