Please solve this quesiton by your own work, thank you. Note: BB=standard Brownian bridge,BM=standard Brownian motion, GP=Gaussian process

H2 A BB is Bo = (B?)to is a sample-continuous GP, having zero mean me(t) = 0 and covariance function CBo( s, t) = s At - st, s,t 2 0. If Z ~ Normal(0, 1) and BM B = (B )to, verify (a) P(B; = B; = 0) = 1; (b) WP := Bt - tB1, t 2 0, defines BB Wo = (WP)t; (c) if Z and Bo are independent, then Wt := Be + Zt, t 2 0, defines BM W = (Wt); (d) law(B B1 = 0) =law(Bo) [Hint: determine Gaussian conditional densities]