Consider the process X(t)=√t​Z where Z has a normal distribution with mean 0 and variance 1 .
(a) Derive the cumulative distribution function F(x)=P{X(t)≤x} and the probability density function of X(t).
(b) Find the variance of X(t+u)−X(t) where u is an arbitrary positive constant.
(c) Argue whether X(t) is a Brownian motion.