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Vd bd e c o a e w x^ ^ l s k Y o o P y z M O z O P O P { / 9 3 2 9 G 0 / @ A3 9 1 / } 3 ?FX;Y(x;y) If fY(y) 6= 0, the conditional pmf of XjY = y is given by fXjY(xjy) def= fX;Y (x;y) fY (y) and the conditional expectation by E(XjY =y)def= å x xfXjY(xjy) and, more generally, E(g(X)jY =y) def= å x g(x)fXjY(xjy);C d) and B= (x y z w), computing ABas a 2 2 matrix, then det(AB), and checking it equals det(A)det(B) If you take a second course in linear algebra you may see slicker ways to understanding why the determinant is multiplicative) Example 33 In the group A (R) = f(a b 0 1) a2R ;b2Rg, the formula for multiplication is (31) a b Y Mx C High Resolution Stock Photography And Images Alamy ‚©‚í‚¢‚¢ ƒAƒŠƒX & ƒyƒ"ƒMƒ" ƒCƒ‰ƒXƒg