For 0s1<s2, we recall that the pair(Ws1,Ws2) is a centered Gaussian vector with variance matrix (s1s1s1s2), and we verify therefore thatWs1Ws2 is also Gaussian with characteristicsE[Ws1Ws2]=s2s1Ws2 and Var[Ws1Ws2]=s1(1s2s1). Denote s=2s1+s2, we have thatWs(Ws1=x1,Ws2=x2) has a Gaussian distribution with conditional meanx=2x1+x2 and conditional variance 4s2s1.

Using this result without proof, justify that the conditional distribution ofWs(Ws1=x1,Ws2=x2,(Wu)u/[s1,s2]) is N(x,4s2s1).