Let X denote the voltage at the output of a microphone, and suppose that X has a uniform distribution on the interval from to –1. The voltage is processed by a “hard limiter” with cutoff values and – .5, so the limiter output is a random variableY related to X by Y = X if |X| ≤ .5 Y = .5 if X> .5, andY = – .5 if X<– .5 .
a. What is P( Y = .5)?
b. Obtain the cumulative distribution function ofY and graph it.
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