To be able to:

(1) Analyze the statistical properties (probability density function (pdf), cumulative distribution function, mean, variance, moments, correlation, covariance, correlation coefficient) of multiple random variables. Identify the concepts of independence, uncorrelatedness, orthogonality of random variables. Identify Gaussian random variables and Central Limit Theorem.

(2) Identify the concept of random process. Compute and interpret the statistical parameters (mean, variance, autocorrelation, autocovariance, crosscorrelation, crosscovariance, correlation coefficient) of random processes.

(3) Identify the concepts of stationarity (strict sense stationarity, wide sense stationarity (WSS)) and ergodicity.

(4) Identify and formulate the power spectral density function for WSS random processes.

(5) Analyze the linear time invariant (LTI) systems with random inputs. Formulate the autocorrelation function and power spectral density function of output in terms of those of input.

(6) Identify Gaussian and Poisson Processes, Poisson Impulses.

(7) Identify white, thermal, shot noise.

(8) Analyze bandpass deterministic signals and modulation techniques. Apply Hilbert transform to bandpass signals.

(9) Apply the principles of deterministic bandpass signals to bandpass noise signals.