In an experiment a random voltage known to be on the interva

In an experiment, a random voltage, known to be on the interval [a, b] is measured. The sample space for the underlying probability experiment is therefore s = {s| a GE s GE b}. A quantizer is modeled by the random variable X which maps voltages in the range a+ib-a/6LEs LT a+(i+l)b-a/6 to the integer (2i - 4) for i = 0,1,2, 3,4, 5. Sketch S and Sx for this model and state whether X is discrete, continuous, or mixed. [Uniform distribution! A fire alarm system is designed to produce a loud tone of frequency 760 Hz. In fact, the alarms are useful as long as the frequency is in the range 650 GE f GE 920 Hz, so that manufacturer accepts this wide tolerance in the production process, but discards all units with frequencies outside this useful frequency band. The salable units have frequencies which are uniformly distributed over 650 GE f GE 920 Hz. A hardware vendor offers to purchase all units with frequencies within plusminus5% of the nominal 760 Hz. What fraction of the salable units would be sold to this hardware vendor?

Solution

Problem 2: S is a continuous random variable and Sx is a mixed random variable.