please explain everything Sampling theorem Based on your algorithm, write a simulation in Matlab to generate i.i.d. samples for the following joint PDF in 3-dimensions: State the 1-dimensional sampling theorem and sketch a proof. Explain the notion of conditional density function, in relation to joint and marginal densities, for dependent variables For a 3-dimensional vector random variable, whose components are statistically dependent, derive a mathematical sampling algorithm as an extension of the 1- dimensional case. fxyz(x,y,z) = k(x+y+z) . supported on the unit cube 0 < x,y,z 51