ECSE 305 Lecture Notes - Fair Coin, Random Variable, Inverse Function

• School: McGill University
• Department: Electrical Engineering
• Course: ECSE 305
• Professor: Ioannis P.

Document Summary

Consider a random experiment described by a triplet (s,f, p ). In applica- tions of probabilities, we are often interested in numerical quantities derived from the experimental outcomes. These quantities may be viewed as func- tions from the sample space s into the set of real numbers r, as in: s s x(s) r. Provided certain basic requirements are satis ed, these quantities are gener- ally called random variables. For instance, the event that the sum is greater or equal to 11 may be expressed concisely as a = {s s : x(s) 11} Random variables are extremely important in engineering applications. They are often used to model physical quantities of interest that cannot be pre- dicted exactly due to uncertainties. Some examples include: voltage and current measurements in an electronic circuit, number of erroneous bits per second in a digital transmission, instantaneous background noise amplitude at the output of an audio ampli er.