The output voltage of a microphone is a Gaussian random vari

The output voltage of a microphone is a Gaussian random variable V with expected value

V = 0V and standard deviation V = 5V. The microphone signal is the input to a limiter

circuit with cut-off value ± 10V. The random variable W is the output voltage of the limiter.

What is the cdf and pdf of W? (Hint: Find W = g(V) first; for the pdf, examine P[W = -10],

and P[W = 10]!)

V is Gaussian (0,5)

Microphone signal has cut off value as

-10<W<10

P(W=-10) = P(w=10) =0

Range of W is 20

Equate this to 3 sigma

sigma = 20/3

Hence W = 4V/3

W is normal with mean =0 and std dev = 20/3