A random noise generator randomly chooses from two distributions.  The first distribution is Gaussian with mean 0, variance 1/4.  The second distribution is uniform from -3 to 3.  The noise generator is set to draw from the Gaussian distribution with probability 0.8.  X denotes an output sample from the generator.  Find the pdf fx(x) for X, and find fx(2).

CDF of :Solution () = P( < ) = P( < , draw from Gaussion distribution)+ P( < , draw from Uniform distribution) = 0.8 × P N 0, < + 0.2 × P(Uniform[−3,3] < )14…

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