Communication, Networking, Signal and Image Processing (CS)

Question 1: Probability and Random Processes

January 2004

3. (30 pts.)

Let $\mathbf{X}\left(t\right)$ be a real continuous-time Gaussian random process. Show that its probabilistic behavior is completely characterized by its mean $\mu_{\mathbf{X}}\left(t\right)=E\left[\mathbf{X}\left(t\right)\right]$ and its autocorrelation function $R_{\mathbf{XX}}\left(t_{1},t_{2}\right)=E\left[\mathbf{X}\left(t_{1}\right)\mathbf{X}\left(t_{2}\right)\right].$

## Alumni Liaison

BSEE 2004, current Ph.D. student researching signal and image processing.

Landis Huffman