Show transcribed image text . Problem 10: Let {B(t) : t ã€‰ 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 ã€ˆ s ã€ˆ t ã€ˆ 1.

. Problem 10: Let {B(t) : t ã€‰ 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 ã€ˆ s ã€ˆ t ã€ˆ 1.