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Variable X conditioned on Y = y, and consequently its expectation E(XY = y), is given Such may be the case in a twostage process, whereby the value of Y is chosen in the first stage, which then determines the distribution of X in the second stage This situation will be very commonD) E(X2e2Y) SOLUTION Using independence and the facts that EX= 1 2, E(X2) = 1 3, EY = 1 and E(Y2) = 2 gives the answers for (a)(c) as E(XY) = 3 2, E(XY) = 1 2, and E(X Y)2 = E(X2) 2EXEY E(Y2) = 4 3 For part (d) we must also compute E(e2Y) = Z 1 0 e2ye ydy= Z 1 0 eydy= 1 Therefore, E(X2e2Y) = 116 Hydrodynamics Reading #4 version 10 updated 1 ©05 A Techet 16 Hydrodynamics Prof AH Techet Potential Flow Theory "When a flow is both frictionless and irrotational, pleasant things happen"FM Page 3 F 104 G High Resolution Stock Photography And Images Alamy ŒC Žû"[ ÈƒXƒy[ƒX 100‹Ï