X is a N (0,0²) random variable. This random variable is passed through a system whose input-output relation is given by y = g(x). Find the PDF or the probability mass function (PMF) of the output random variable Y in each of the following cases: a) Square law device, g(x) = ax² b) Limiter, c) Hard limiter, (-b, g(x)=b, X, a, g(x)= =0, x≤-b xzb. |x|0 x=0.

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X is a N(0, 0²) random variable. This random variable is passed through a
system whose input-output relation is given by y = g(x). Find the PDF or the probability mass
function (PMF) of the output random variable Y in each of the following cases:
a) Square law device, g(x) = ax²
b) Limiter,
c) Hard limiter,
g(x) =
-b,
b,
x,
a,
g(x)=0,
.b,
x ≤-b
x ≥b.
|x| <b
x>0
x= 0.
x < 0
Transcribed Image Text:X is a N(0, 0²) random variable. This random variable is passed through a system whose input-output relation is given by y = g(x). Find the PDF or the probability mass function (PMF) of the output random variable Y in each of the following cases: a) Square law device, g(x) = ax² b) Limiter, c) Hard limiter, g(x) = -b, b, x, a, g(x)=0, .b, x ≤-b x ≥b. |x| <b x>0 x= 0. x < 0
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