Hey mathman.
Hint: Use the property of a Brownian motion that if if B_a(t) and B_b(t) are brownian motions over disjoint times then they are both independent.
Hi!!! I hope someone can help me with the following exercise...
n>=1, 0=t_{0}<t_{1}<...<t_{n}, a_{1},a_{2},...,a_{n} ε R. Show that the random variable a_{1}*B(t_{1})+...+a_{n}*B(t_{n}) is normally distributed and find its mean value and variance.