Q9. Let us assuming the voltage output of a microphone is a Gaussian random variable V with expected value µy = 0 and standard deviation ơy = 5 V. The microphone signal is the input to a limiter circuit with cutoff value ±10 V. The random variable W is the output of the limiter: 10 -10 V < -10, -10 < V < 10 V > 10. W = g(V) = V -10 10 -10 10 V From this example, find the following A. Find the PDF of W? B. Find the CDF of W?

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Q9. Let us assuming the voltage output of a microphone is a Gaussian random variable V with expected
value Hy = 0 and standard deviation ơy = 5 V. The microphone signal is the input to a limiter
circuit with cutoff value ±10 V. The random variable W is the output of the limiter:
10
-10 V < -10,
-10 < V < 10
V > 10.
W = g(V) =
V
-10
10
-10
10
V
From this example, find the following
A. Find the PDF of W?
B. Find the CDF of W?
Transcribed Image Text:Q9. Let us assuming the voltage output of a microphone is a Gaussian random variable V with expected value Hy = 0 and standard deviation ơy = 5 V. The microphone signal is the input to a limiter circuit with cutoff value ±10 V. The random variable W is the output of the limiter: 10 -10 V < -10, -10 < V < 10 V > 10. W = g(V) = V -10 10 -10 10 V From this example, find the following A. Find the PDF of W? B. Find the CDF of W?
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