where 0 (a) Show that the marginal distributions tire given by fx(x) af1(x) (1 a)f2(x) and f Icirc sup3 (x) ag1(y) (1 a)g2(y) (b) Show that X and Y are independent if and only if f1(x) f2(x) g1 (y) g2 y) 0 (X, Y) afi()gi(v) (1a)f()g2(v),

Question: where 0 (a) Show that the marginal distributions tire given by fx(x) = af1(x) + (1 - a)f2(x) and fÎ³(x) = ag1(y) + (1 -

where 0 (a) Show that the marginal distributions tire given by fx(x) = af1(x) + (1 - a)f2(x) and fÎ³(x) = ag1(y) + (1 - a)g2(y).
(b) Show that X and Y are independent if and only if |f1(x) - f2(x)][g1 (y) - g2{y)] = 0.

(X, Y) ~afi()gi(v) (1a)f()g2(v),

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