Image: Probabilities of functions of normal vectors

Description: a: Probability density of a function cos⁡x2{\displaystyle \cos x^{2}} of a normal variable x{\displaystyle x} with μ=−2{\displaystyle \mu =-2} and σ=3{\displaystyle \sigma =3}. b: Probability density of a function xy{\displaystyle x^{y}} of two normal variables x{\displaystyle x} and y{\displaystyle y}, where μx=1{\displaystyle \mu _{x}=1}, μy=2{\displaystyle \mu _{y}=2}, σx=.1{\displaystyle \sigma _{x}=.1}, σy=.2{\displaystyle \sigma _{y}=.2}, and ρxy=.8{\displaystyle \rho _{xy}=.8}. c: Heat map of the joint probability density of two functions of two correlated normal variables x{\displaystyle x} and y{\displaystyle y}, where μx=−2{\displaystyle \mu _{x}=-2}, μy=5{\displaystyle \mu _{y}=5}, σx2=10{\displaystyle \sigma _{x}^{2}=10}, σy2=20{\displaystyle \sigma _{y}^{2}=20}, and ρxy=.495{\displaystyle \rho _{xy}=.495}. These are computed by the numerical method of ray-scanning.
Title: Probabilities of functions of normal vectors
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Author: Dvidby0
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