Let X Y and Z be a set of independent
Let X, Y and Z be a set of independent, zero- mean, unit- variance, Gaussian random variables. Form a new set of random variables according to
U = X
V = X + Y
W = X + Y +Z.
(a) Find the three one- dimensional marginal PDFs, fU (u) Fv (v), and fW (w).
(b) Find the three two- dimensional joint PDFs, fU, V (u, v) fV, W (v, w) and fU, W (u, w).
(c) Find the three- dimensional joint PDF of U, V, and W fU, V, W (u, v, w).
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