Gaussian random variable with PDF
Hi, I had a question I am hoping someone can give me some pointers on.
Question: Guaussian random variable X with PDF, fx(x)=1/(sqrt(2*pi))*e^(-x^2/2) ; -infinity< x < +infinity.
a) The Gaussian is passed through a square law device with output Y=X^2. Find the PDF of Y.
b) THe Gaussian is "passed through a full wave rectifier with output Y=absolutevalue(X). Find the PDF of Y
*See attached image for hint given
Second part to question: Consider the three level limiter shown in the figure (attached)
a)Find the PDF of Y if X is the Gaussian PDF of the previous problem. Express answer in terms of the CDF of X given by phi(x)=integral from t=-infinity to t=x of 1/(sqrt(2*pi))*e^(-t^2/2) dt
b)Sketch both the PDF , fY(y) and the CDF, FY(y) for the random variable Y.
Thanks for whatever help I can get!