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