Show transcribed image text . Problem 10: Let {B(t) : t 〉 0} be a Brownian Motion with B(0) 0. The following conditional stochastic process {B(t), 0-t-1B(1) 0} is called a Brownian Bridge. Prove that the Brownian Bridge is a Gaus- sian Process. Hence, calculate the mean EB(t)B(1) = 0] and covariance Cov [B(s). B(t) 3(1) = ì´ for 0 〈 s 〈 t 〈 1.
. Problem 10: Let {B(t) : t 〉 0} be a Brownian Motion with B(0) 0. The following conditional stochastic process {B(t), 0-t-1B(1) 0} is called a Brownian Bridge. Prove that the Brownian Bridge is a Gaus- sian Process. Hence, calculate the mean EB(t)B(1) = 0] and covariance Cov [B(s). B(t) 3(1) = ì´ for 0 〈 s 〈 t 〈 1.
