1. Random Processes - MIT

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Design Principles for Ocean Vehicles Prof. Techet Spring 2005 1. Random Processes A Random variable,()x , can be defined from a Random event, , by assigning values ix to each possible outcome, iA, of the event. Next define a Random process , ()xt ,, a function of both the event and time, by assigning to each outcome of a Random event, , a function in time, 1()xt, chosen from a set of functions, ( )ixt. 111222()()()nnnApxtApxtApxt MMM (6) This menu of functions, ( )ixt, is called the ensemble (set) of the Random process and may contain infinitely many ( )ixt, which can be functions of many independent variables.

Next define a Random Process, x()ζ,t, a function of both the event and time, by assi gning to each outcome of a random event, ζ, a function in time, x 1 () t , chosen from a set of functions, ( ) x i t .

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