Let V : R n → → R be a differentiable function and X be a random vector taking values in R n , f X be the probability density function of X and δ δ ( ⋅ ⋅ ) be the Dirac delta function. It is possible to use the formulas above to determine f Y , the probability density function of Y = V ( X ) , which will be given by f Y ( y ) = ∫ ∫ R n f X ( x ) δ δ ( y − − V ( x ) ) d x .