3. Suppose that X and Y are independent with X N(0,4). Let U = X + Y and V = X – Y. N(0, 1) and Y~ a) Find the joint probability density function of (U,V), fu,v(u, v). b) Are U and V independent?

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3. Suppose that X and Y are independent with X ~ N(0, 1) and Y~
N(0,4). Let U = X + Y and V = X - Y.
a) Find the joint probability density function of (U, V), fu,v(u, v).
b) Are U and V independent?
Transcribed Image Text:3. Suppose that X and Y are independent with X ~ N(0, 1) and Y~ N(0,4). Let U = X + Y and V = X - Y. a) Find the joint probability density function of (U, V), fu,v(u, v). b) Are U and V independent?
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