Let n>=1, times 0=t0<t1<...<tn, constants a1,a2,...,an ε R. Show that the random variable a1B(t1)+...+anB(tn) is normally distributed and find its mean value and variance. (B is a brownian motion)
Since B is a Brownian Motion, E(B(t)-B(s))=0, s<t, and B(0)=0, can we say that E(a1B(t1)+...+anB(tn))=E(a1(B(t1)-B(t0)))+...+E(an(B(tn)-B(t0)))=0 ???
And how can I find Var(a1B(t1)+...+anB(tn))????
Since B is a Brownian Motion, E(B(t)-B(s))=0, s<t, and B(0)=0, can we say that E(a1B(t1)+...+anB(tn))=E(a1(B(t1)-B(t0)))+...+E(an(B(tn)-B(t0)))=0 ???
And how can I find Var(a1B(t1)+...+anB(tn))????