Let X denote the voltage at the output of a microphone,and suppose that X has a uniform

Chapter 4, Problem 18

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Let X denote the voltage at the output of a microphone,and suppose that X has a uniform distribution on theinterval from 21 to 1. The voltage is processed by ahard limiter with cutoff values 2.5 and .5, so the limiteroutput is a random variable Y related to X by Y 5 Xif |X| # .5, Y 5 .5 if X . .5, and Y 5 2.5 if X , 2.5.a. What is P(Y 5 .5)?b. Obtain the cumulative distribution function of Y andgraph it.

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