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In this question assume that {B(t), t 2 0} is the standard Brownian motion (BM). (a) The Brownian bridge on [0,1] is defined as X (t) = B(t) - tB(1), t e [0, 1] . This process is clearly a Gaussian process. Find its mean and covariance functions. 2 (b) With the Brownian bridge defined in question (a), show that the process {W (t) : te [0, 1]} defined by t W (t ) = (1+t ) X Itt Ost