O'Reilly logo

Probability and Stochastic Processes: A Friendly Introduction for Electrical and Computer Engineers, 3rd Edition by David J. Goodman, Roy D. Yates

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

6

Probability Models of Derived Random Variables

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 r0 ohm resistor is a random variable X, the power dissipated in that resistor is Y = X2/r0. 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 = X2. 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 ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required