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With the joint pdf of N-variate Gaussian density function below, derive the bi-variate Gaussian density function. (10points) fXXX ( 1, X2 , " " , X'N ) 1/2 x - X ] [ C * J' [ x - X = N/2 exp 2 : N - variate Gaussian densityThis exercise should be done two ways: by hand and using technology where possible. Let 1 A 01023 12 ' 12 020' ' '2 6 0 Evaluate the following. AB ll II 5-2.1 Classify each of the following random processes as continuous, discrete, or mixed. a) A random process in which the random variable is the number of cars per minute passing a given traffic counter. b) The thermal noise voltage generated by a resistor. c) The random process defined in Problem 5-1.2. d) The random process that results when a Gaussian random process is passed through an ideal half-wave rectifier. e) The random process that results when a Gaussian random process is passed through an ideal full-wave rectifier. 206 CHAPTER 5 . RANDOM PROCESSES () A random process having sample functions of the form X (1) = A cos ( Bt + 0) where A is a constant, B is a random variable that is exponentially distributed from 0 to oo, and e is a random variable that is uniformly distributed between 0 and 2x