# Math Help - Gaussian process

1. ## Gaussian process

If I have the process $(X_t)_{t\ge0}$, $X_t=(1-t)\int_0^t\frac{dB_s}{1-s}$, $B_s$ 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?

2. This isn't a Gaussian process, as $X_1=0$ a.s.

3. The question was for $(X_t)_t$, where $0\le t<1$, I wrote it wrong in the first post. Thank you for answering.