6. (Total: 10 pts) Suppose W(t) represents a Wiener process with parameter o'. Recall properties of the Wiener process (Brownian motion): I. W(O) = 0. II. W(t1) - W(t2) ~ N(0, o' (t1 - t2)), t1 > tz. III. W(t) has independent increments, that is if (1, t2) and (ts, t4) are non-overlapping intervals, W(h) - W(tz) and W(ts) - W(t) are independent. Let X(t) = W(ct) for some constant c > 0. We will show that X (t) is also a Wiener process. (a) (1 pts) Show that X(t) satisfies property I. (b) (3 pts) Show that X(t) satisfies property II. (c) (4 pts) Show that X(t) satisfies property III. (d) (2 pts) Find the parameter of this Wiener process. Note: This is called the self-similarity property of the Wiener process