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. \[\int_{-\infty}^{\infty}f\left(x\right)dx=1\] ...

Abstract: Alice selects an arbitrary pdf f and uses a stochastic encoder to generate a prefix-free codeword M, which is sent to Bob so that he can generate a single instance of the random variable X ~ ...

Abstract: We consider a setup in which Alice selects a pdf ƒ from a set of prescribed pdfs P and sends a prefix-free codeword W to Bob in order to allow him to generate a single instance of the random ...

Probability theory forms the mathematical backbone for quantifying uncertainty and random events, providing a rigorous language with which to describe both everyday phenomena and complex scientific ...