There are many situations in which we observe one or more random variables and use their values to compute a new random variable. For example, when voltage across an *r*_{0} ohm resistor is a random variable *X*, the power dissipated in that resistor is *Y* = *X*^{2}/*r*_{0}. Circuit designers need a probability model for *Y* to evaluate the power consumption of the circuit. Similarly, if the amplitude (current or voltage) of a radio signal is *X*, the received signal power is proportional to *Y* = *X*^{2}. A probability model for *Y* is essential in evaluating the performance of a radio receiver. The output of a limiter or rectifier is another random variable that a circuit designer may need to analyze.

Radio systems also provide practical examples of functions of two random variables. For example, we can describe the amplitude of the signal transmitted by a radio station as a random variable, *X*. We can describe the attenuation of the signal as it travels to the antenna of a moving car as another random variable, *Y*. In this case the amplitude of the signal at the radio receiver in the car is the random variable *W* = *X*/*Y*. Other practical examples appear in cellular telephone base stations with two antennas. The amplitudes of the signals arriving at the two antennas are modeled as random variables *X* and *Y*. The radio receiver connected to the two antennas can use the received signals in a variety of ways.

It can choose the signal with the larger amplitude and ignore ...

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