# Question

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).

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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