Question: A nonlinear system has input X and output Y. The pdf for the input is Gaussian as given in Problem 6.16. Determine the pdf of

A nonlinear system has input X and output Y. The pdf for the input is Gaussian as given in Problem 6.16.

Determine the pdf of the output, assuming that the nonlinear system has the following input/output relationship:

(a) aX, X >0 Y = 0,

When X < 0, what is Y? How is this manifested in the pdf for Y?

(b) Y = |X|;

aX, X >0 Y = 0,

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