TABLE OF CONTENTS A random variable x is a static variable defined on random outcomes, "static" in the sense that time is fixed for an RV: an RV is a function of random outcome ?, x( ?), but time is not an argument of this function.
A stochastic process x (t) is the random variable x extended into another dimension t. To be rigorous in notation, we might write a stochastic process as x( ?, t), where x is a function of two variables, time t and random outcome ? For simplicity, however, x( ?, t) is written x (t) as the random variable x( ?) is written x.
To define it in more general terms, a stochastic process is a set of random variables arranged in time as follows:
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If the interval (t a, t b) is a continuum of time, the stochastic process is referred to as a continuous process; if the interval (t a, t b) is a set of discrete time points, t i's, the stochastic process is referred to as a discrete process.
A useful concept to remember is that, once the time t is fixed at a specific value, say t *, the stochastic process yields a random variable; that...
