Independence and exchangeablility Independent random variables cont'd Example: let Y1, . .. , Ym | /, o ~ Normal(/, o), write out the joint density of f( Y1, . . . , Yn | /, ). (Hint: the Normal pdf is f(Y; = yi | /, g) = exp(- 202 ") ) n f( Y1 = M1, " . . ; Ym = yn | 4, o) = i=1 n = (vi - 1)2 exp i=1 V2102 202 1 E(vi - 1)2 exp V2102 2025. (Distribution preview) Let X1, . .., Xn ~ Normal(ux, ox), and Yl, . .. , Ym iid Normal(ly, OY), and assume all X's and Y's are independent. Write out the joint density: f(X1 = 11, . . . , Xn = In, YI = yl, . .. ; Ym= ym | Hx, HY, Ox, Or)