*4. Let Y1, Y2 be random variables and h(Y1, Y2) be a transformation that is monotone in yı for each y2 on the joint support. Let h-l denote a marginal inverse transformation such that Y1 = h-1(u; y2). Show that the density of U = h(Y1,Y2) is: g(u) = | f (h- (u; y2), 92) | d -h'(u; y2) dyz du

MATLAB: An Introduction with Applications
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*4. Let Y1, Y2 be random variables and h(yı, Y2) be a transformation that is monotone in y1 for
each y2 on the joint support. Let h-1 denote a marginal inverse transformation such that
Y1 = h-1(u; y2). Show that the density of U = h(Y1,Y2) is:
g(u) = | f (h- (u; y2), Y2)
d
h' (u; y2)| dy2
du
Transcribed Image Text:*4. Let Y1, Y2 be random variables and h(yı, Y2) be a transformation that is monotone in y1 for each y2 on the joint support. Let h-1 denote a marginal inverse transformation such that Y1 = h-1(u; y2). Show that the density of U = h(Y1,Y2) is: g(u) = | f (h- (u; y2), Y2) d h' (u; y2)| dy2 du
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