Question

Problem # 8.

a) Let X be a continuous random variable with known CDF FX(x). LetY = g(X) where g(·) is the so-called signum function, which extracts the sign of its argument. In other words,

g(X) = { -1 x<0, 0 x=0, 1 x>0 }

Express the PDF fY (y) in terms of the known CDF FX(x).

b) Let X be a random variable with PDF:

fX(x) = { x/2 0 <= x < 2, 0 otherwise}

Let Y be the output of the “clipper”:
Y=g(X)= { 0.5 X <= 1, X X>1 }

Find:
The probability P [Y = 0.5],  The PDF fY (y)

Answer 1