Communication, Networking, Signal and Image Processing (CS)
Question 1: Probability and Random Processes
August 2012
Question
Part 1. 25 pts
$ \color{blue}\text{State and prove the Chebyshev inequality for random variable} \mathbf{X}\text{ with mean}\mathbf{\mu}\text{ and variance } \mathbf{\sigma^2} \text{. In constructing your proof, keep in mind that} \mathbf{X} \text{ may be either a discrete or continuous random variable} $
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Part 2. 25 pts
$ \color{blue} \text{Show that if a continuous-time Gaussian random process } \mathbf{X}(t) \text{ is wide-sense stationary, it is also strict-sense stationary.} $
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