Let W={Wt:t=0} be a Brownian motion on (O,F,F=(Ft)t=0,P). Fix a,ß?R and consider the following…

Let W={Wt:t=0} be a Brownian motion on (O,F,F=(Ft)t=0,P). Fix a,ß?R and consider the following SDE:

dXt=ß-XtT-tdt+dWt,0

and

X0=a,XT=ß.

A solution to this SDE, with the given boundary conditions, is called a Brownian bridge. By applying Ito’s lemma to Yt:=f(t,Xt)=XtT-t, solve this SDE and find the distribution, mean, and variance of Xt, where 0</pclass=”msonormal”>