Question: 5. Let Z,,; (IX = 1, . .. , m; i = 1, .. . , p) be independently distributed as N(O,1), and let Q

5. Let Z,,; (IX = 1, . .. , m; i = 1, .. . , p) be independently distributed as N(O,1), and let Q = Q(Y) be an orthogonal m X m matrix depending on a random variable Y that is independent of the Z 's, If Z;; is defined by ( ZD . .. Z:'i) = ( Zli . .. Zmi)Q/• 489 then the Z;; are independently distributed as N(O.I) and are independent of Y. [For each Y. the conditional distribution of the (Zli' " Zmi)Q /(y). given Y = y. is as stated .]

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