If I have the process $\displaystyle (X_t)_{t\ge0}$, $\displaystyle X_t=(1-t)\int_0^t\frac{dB_s}{1-s}$, $\displaystyle B_s$ is the Brownian motion, how can I show that is a Gaussian process? After this how can I compute its mean and covariance function in the easiest way?